Did you read the tech bulletin I posted and check that connector? It could just be a bad connection between the PCM and the transaxle.

So you brought the car and test drove it and it shifted through all the gears without any issues, no noticeable slipping or anything? It could have develop the problem afterwards without the owner knowing anything. However, if the owner knew about any problems with the car then they should have been told to you; it does not matter if it was a private owner. However, you might have to sue in small claims court for redress.

Now, if you have not checked out that tech bulletin then you should do so because that is a known issue with the transaxle.

Now, your transaxle might not be starting out in first gear, it could be starting out in second gear, the trans might be in limp mode. I will post part of a test article and hope it is within the forum rules; if it is not, then I am sure the moderators will let me know .

Basics of the 4T60-E (4T65-E)
Automatic Transmission in Your GM Vehicle

Depending on the year of your GM vehicle, it'll either use the 4T60-E or the 4T65-E automatic transmission (technically, it'* called a transaxle). These two are not interchangeable.

Here are some more specifics:

4T60-E

Introduced in 1991 and used in almost all of GM'* front wheel drive (FWD) vehicles up until the late 1990'*. The 4T60-E'* upshifts and downshifts are computer controlled by way of two shift solenoids, as such... it doesn't have a kickdown cable.
There are several different versions of the 4T60-E and most of their internal electronics are NOT compatible with each other... not to mention that the Final Drive Ratio will not be the same.
If replacing the complete transaxle, you should only replace with a unit that'* verified to be the same. Using the wrong 4T60-E unit will cause you a head-ache, since the transmission will not function correctly, if at all.

4T65-E

Introduced in 1997 and eventually replaced the 4T60-E. This automatic transaxle was used up until 2011.
Not interchangeable with the 4T60-E.

NOTE: The following link will help you in identifying the 4T60-E or 4T65-E transmission in your vehicle: GM FWD Transmission ID Charts (at: Sinister Performance, LLC.)

Let'* now take a look at the most common types of failure in the next heading.
Two of the Most Common Transmission Failures

The most important thing to know, when trying to troubleshoot a transmission problem, is that the 4T60-E (and 4T65-E) automatic transmission usually fails in one of two ways:

Transmission is ‘slipping’.
A transmission that'* ‘slipping’ indicates internal mechanical failure.
A low level of transmission fluid (usually due to a transmission fluid leak) can also cause the transmission to ‘slip’.
In case you're wondering: ‘slipping‘ can be best described as having the transmission go into neutral, although it'* in drive, and not move the vehicle no matter how much you step on the accelerator.
Transmission does not shift out of 2nd gear.
This generally happens when the PCM senses an electrical problem and commands the transmission to stay in what is known as ‘Limp In Mode’.
In ‘Limp In Mode’, the automatic transmission will not downshift or upshift at all.
The usual cause of this condition is an electrical issue, like a bad shift solenoid... although some internal mechanical problem/damage can also cause this.

Each one of the above conditions has a specific cause and in the next sections, we'll explore this a bit more in-depth.
How Can I Tell If It'* Just a Solenoid Failure?

The electronically controlled 4T60-E/4T65-E has several solenoids and sensors that the PCM needs to control the upshifts and downshifts. If any one of these sensors/solenoids fail or the fuse(*) that supplies the solenoids gets blown... the transmission will go into ‘Limp In Mode’.

What makes it pretty easy to tell if the automatic transmission failure is just a solenoid related issue... due to the fact that the transmission doesn't ‘slip’.

Here are some very specific symptoms you'll see when a transmission solenoid goes bad:

The PCM is also gonna' light up the Check Engine Light (CEL) and store a specific shift solenoid diagnostic trouble code (DTC). All transmission diagnostic troubles codes start with: P07XX (the XX being the last 2 digits of the DTC).
You'll see one or several of the following transmission diagnostic trouble codes:
P0700: Transmission Control System Malfunction
P0751: Shift Solenoid A Malfunction
P0755: Shift Solenoid B Malfunction
The above are just some of the transmission diagnostic trouble codes you'll see... since there are quite a few that I didn't have space to list.
The speedometer does not work and you might have one of the following trouble codes:
P0500: Vehicle Speed Sensor Malfunction
P0501: Vehicle Speed Sensor Range/Performance
P0502: Vehicle Speed Sensor Low Input
P0503: Vehicle Speed Sensor Intermittent/Erratic/High
Your 4T60-E/4T65-E automatic transmission will stay in only one gear no matter what the vehicle speed.
As you accelerate your vehicle, it feels very underpowered. This is due to the fact that the transmission is starting out in 2nd gear.
At speeds over 35 MPH, the engine feels like it'* over-revving. This is also due to the fact that the transmission is staying in 2nd gear and the gear ratio provided by 2nd gear is gonna' keep the engine working pretty hard at any speed above 35 MPH.

Remember, what will tell you that you have a solenoid or internal transmission sensor problem is:

You'll have a specific transmission diagnostic trouble code (or a Speed Sensor diagnostic trouble code).
The automatic transmission does not ‘slip’, no matter how many times you road test your vehicle.
The 4T60-E stays/4T65-E in ‘Limp In Mode’ (note: see Transmission with Both Solenoid Failure and Internal Damage).

Let'* turn the page and find out more about the specific symptoms a 4T60-E/4T65-E with internal damage...

One thing to understand is that trouble codes are just guidelines; too many shops think that trouble codes are definite but they are not. Failures don't always result in trouble codes and trouble codes don't always indicated the correct failure; like my code 18 had nothing at all to do with the cam/crank position sensor circuit and I was chasing that dog all over the place.

I know a mechanic in California that is in my opinion one of the top mechanics I have ever had the pleasure to come across, he reminded me of me Dad who was top of the game when it came to working on cars. I can PM you his email address if you like.

I did check the wiring. Pulled it apart and it looks ok. Is there a trans relay?

Also, the tech bulletin was not there in your one post so I couldn't look at it.

Is there a trans relay?

No I believe the power supply for the shift solenoids is provided through the ignition switch. You need to pull the transmission plug and see if you have 12v at the pink wire with the key on. Problem is that if the transmission solenoids lose power the transmission defaults to 2nd gear not 1st.

I disagree....codes are a valuable tool......but only if you know how to use them....to assume the problem is the part the code is named after is a huge mistake......that code can be caused by anything in the circuit, or anything that affects the operation of the circuit......if you do not follow the trouble tree to the letter, you are just wasting time and parts...

The problem is he doesn't have a scanner he can look at live data or comand the transmission into gear, nor do we have a wiring diagram or trouble tree. So I believe he is searching for something obviously wrong. As I stated in a earlier post you need to get you hands on a high end scanner and a wiring diagram to properly diagnose this thing.

I agree.....a lot of posters just assume we can diagnose their problems on the internet.......the cars today are so electronically oriented, that without the proper tools and testing, they are almost impossible to repair.....too many times they get advice, like my car had the same problem, and this fixed it.....

When you get into transmission problems, unless he followed our advice step by step, and had the proper tools to do it, his only real course of action would be to go to a tranny shop or garage that he has confidence in....

Hell, I can't even diagnose my own car at home, without the proper tools....

I noticed that if I go 40 mph The engine is at around 5,000 rpms. Does that sound like 1st gear or second gear?