Here is a website that I found that showed a cheap fix with a simple resistor and cutting two wires. I don't know if this is a great fix but it sounds reasonable if it works.
GM Passlock Security Fix

I looked and see that the cost of the replacement PassLock sensor is about $75.00. It is just how hard is it to get to the sensor that I am concerned with, seems like you have to go through the center console and take out the radio and reach in that way, is that correct?

The cutting two wires and adding a resistor only bypass the key/ignition part of the system.
The Theft Deterrent Module still has to see the 60hz or 30Hz frequency depending on the year of the vehicle, yours should need to see 60Hz.
In my Park Ave it was way up in behind the dash, not sure where it is in your car, possibly in the same location..

From reading the article on the cutting of the two wires and inserting the resistor it is a bypass of the PassLock sensor, the key is still needed to use the normal ignition switch circuit. No more security but regular key starting from what the article is saying. I would assume the resistor is sending the signal as if the sensor is working and giving the signal to the PCM. I think I would rather put in a new sensor myself, but the resistor would be a much cheaper if not smart move.

Yeah the key is still needed to turn the ignition switch, but all you are doing is bypassing the ignition switch part, that reads the resistance of the key, then sends it down to a terminal with a bunch of wires near the driver side feet area on some cars, from there it goes to the TDM, if the TDM is what is bad, then the resistor switch trick cannot fix that part.

If you can find the wire they mention, and follow it to its terminal which I mentioned, then as soon as it won't start you could probe the two wires at the terminal and measure their resistance, it should match the resistance you get when you measure the resistance of the pellet on your key.
The wire should be orange coated, with two small white wires coming from out of the sheathing, and going into the main terminal somewhere under the dash, around the driver side left foot area...
Or if you can find the two wires from the ignition that go into the TDM, then you could add the resistors there, but if the ignition switch is the issue, and you do not cut the wire coming from it, then you will not have the TDM seeing the right resistance, and it will never start. Because it would be seeing 2x the resistance from time to time, because the key plus the resistors you'd add would effectively double the resistance..

You can put the resistor in like this if you choose, but I'd rather solder it is to be safe.
If it was just your ignition switch faulty, then this would work as long as the wire from there to the ignition switch was disconnected, or cut.

As long as the problem is truly the PassLock sensor that seems like the best thing to just change. The ignition switch itself shouldn't be the problem it seems. From what I am reading it appears the easiest access to the sensor is through the console after taking out the radio. I have the manual for my Montana that should have the same basic wiring harness as the Alero so I'll look in there for the wiring schematic.

If the 2001 is like the 2000 Alero this may help.

""Pry up the plastic molding from around the radio/heater A/C controller and from around the gear shifter. Detach the heater A/C module from the molding by removing the four 7mm hex bolts from the backside. Take out the three 7mm hex bolts to loosen the radio. Put the key in the ignition and turn to "on" position, apply brake, and shift into "drive" or lower gear. Turn the heater A/C module to the left, sideways orientation, and pull out the radio. Disconnect main wiring harness from back center of radio if there is not enough slack to take the radio out past the plastic molding. Leave the antenna connected. Look inside and to the left at the back of the ignition cylinder assembly. Locate the thin yellow wire, which is bundled alongside the thin white and the thin black wire.""

But again, if you mess with that wire, as in cut it and wire in resistors that match your key pellet, then that fix is only for a bad ignition switch.

The TDM that would be the culprit if you rule out an intermittent short in the ignition switch wiring.
I tried to find more info on exactly where the TDM is, but all I could find were suggestions that it is where I mentioned, behind the IP Panel on the passenger side, you pretty much have to turn upside down to get down in there to get to it, at least I did.
I think mine was somewhat near the Body Control Module..
I am a little tired atm so my memory is not as sharp as it should be, badly in need of a long nap!

This is what your Theft Deterrent Module looks like.


Here is what the wiring to the switch that I am talking about looks like.


I still would get a multimeter, and when the car won't start, then set the multimeter to ohms, and find that connection coming from the ignition switch, the connector in the switch above is what I am talking about.
With the key in measure the ohms from the 2 wires contacts via back probing them, then measure the resistance from the contact on both sides of the keys pellet, then compare resistance values, they should be really close to the same.
Values should be one of the listed values in this pic.

William,
when you say to measure the resistance on the key that I have a question about. Do you just measure across the cut part of the key or do I some how have to get to the sealed chip inside the plastic part on the key? I know on my Montana that had a different type of key it was covered in a rubber type material on the Alero it is a hard plastic, not sure how you could measure anything without destroying the key itself. I really don't think it is the ignition switch itself as it always will turn on the dash lights and warning lights on the dash, just won't start the car and the security light flashes. So that makes me think the PassLock sensor would be the culprit more than the switch. I've never had to pull the radio so I'll have to see what kind of fasteners GM is using there to get the plastic fascia off around the radio, don't want to break the plastic parts as that stuff is so damned expensive to replace. I have a DMM so no problem measuring the impedance on the key once I know how to measure it. Thanks for all the help, your pictures will surely help.

Steven

One more thing that may clue you in. I have two keys for the car with remote fobs that are supposed to open the door locks or lock the doors. With new batteries in them neither one will work on the remote, it will not reconnect even after a new battery and the relearn process for the fob. I'm not sure where the connection is made between those fobs and the car, is that through the radio or is that also with the PassLock sensor? This may be something related or have nothing to do with anything. I just stopped using the remote and just open the door with the key and lock the door from the door switch before I leave the car. Thanks again.

Ahhh wait, I thought they used PK 2 up till 2004, maybe some got PK 3 before then.
Does your key look like this key?
If so you measure from the small metal contact point I on each side, I circled what I am talking about..


Sounds like hte TDM is the issue, since the Key Fob won't reprogram, but the only way to be sure would be to have a dealer scan it when it has the issue.

No, that looks like the key from my 2001 Montana. The Olds has a larger hard plastic cover over the end of the key and is cut on both sides of the key not like that key which is only cut on one side. It has symmetrical cuts on both edges of the key.