Do you still have your owner'* manual?

Check what you have for a Security system...PK I, PK II, PK III, or PassLock.....

I think you have PassLock.......but PassLock does not use a chip on the key.....so there is confusion here, when you say one key has a chip, and the other two don't.....

When you say chip, what kind of chip? Is it a black resistor chip in the middle of the shaft key with metal contacts on each side? Like this?

I don't think a bad chip/no chip would physically prevent the key from turning. The situation the OP is describing would indicate something broken inside the lock cylinder.

The only reason I ask about the chip, which is confusing, is to establish which Security system he has....depending on that outcome, we can try to tell him how to go about a fix....

Owners manual says PassLock

Looking at the picture you posted, there is no chip visible on the key. Nor is there a visble chip on the top of the key.........i believe you are correct. There is no chip, but the owners manual do say "Passlock".

OK, now that we have established there is no chip or transponder involved, we can assume it is PassLock....

Seen this many times in PassLock lock cylinders.....the tumblers go bad, and the lock cylinder has to be replaced......

Were you having previous problems where you had to jiggle the key to get it to turn sometimes?

The lock cylinder is part of the PassLock sensor...together, they slide into the ignition switch......

I'm not sure on the intrigue, but whenever I had to replace the PassLock sensor on a Grand AM, I had to remove the fascia plate to the radio, to get to 2 bolts, holding it in place....then I had to remove the instrument cluster, to get access to the cylinder/ignition switch.....to remove the lock cylinder/sensor from the ignition switch, you have to rotate the key, and depress a tab to separate the sensor from the ignition switch....problem is, your key won't turn....this means you are going to have to drill a hole through the casting to break the retaining spring, so the sensor can separate from the ignition switch.....it'* hard to describe where this hole should be drilled....you will need access to a manual to know the correct spot.....you will get a new sensor/cylinder that comes with new tumblers....you probably will need a locksmith to install the tumblers into the lock cylinder, to match your key......

I really appreciate you taking the time to provide this "valuable" information. I ordered a new ignition cylinder from Amazon - APDTY 035813 Ignition Lock Cylinder w/New Keys And Passlock Chip (Fixes Security Light)(D1493F; 25832354; 15822350; US286l)(Dash-Mounted)

These directions were included:
GM Passlock™ Ignition Cylinder Replacement Instructions
Removal and installation:
1. Remove Trim panel around radio, usually held in with snap-in clips, some vehicles may have a screw or two
2. Unbolt and remove the radio to gain access to the back of the lock cylinder
3. Press the small release tab (see pictures) While turning key to the ON Position
4. Slide out old lock cylinder
5. Installation is the reverse of the above procedures, see below for the relearn procedure
Pre-Relearn Procedure Check List
1. Fully Charge Battery
2. Clear all Diagnostic Trouble Codes (DTC). Record and/or repair your DTCs before clearing. You can clear the codes by disconnecting the battery for 10 minutes.
Relearn Procedure
1. Turn ON the ignition, with the engine OFF
2. Attempt to start the engine, then release the key to ON (vehicle will not start)
3. Observe the SECURITY telltale, after approximately 10 minutes the telltale will turn OFF
4. Turn OFF the ignition, and wait 5 seconds
5. Repeat steps 1 through 4 two more times for a total of 3 cycles/30 minutes (The vehicle is now ready to relearn the Passlock™ Sensor Data Code and/or passwords on the next ignition switch transition from OFF to CRANK)
6 Start the engine (the vehicle has now learned the Passlock™ Sensor Data Code and/or password)
7 With a scan tool, clear any DTCs if needed (history DTCs will self clear after 100 ignition cycles)
IMPORTANT The vehicle learns the Passlock™ Sensor Data Code and/or password on the next ignition switch transition from OFF to Crank. You must turn the ignition OFF before attempting to start the vehicle.

I took it to a mechanic and he installed it for me. Thank you again "Certainly know your stuff" !!! Great Assistance! Hope this thread will be helpful to someone else.