95 cutlass supreme not cranking

i have a 95 cutlass supreme that wont turn over now i have replaced the ignition switch with no luck, all of my fuses and fusable links are good and i can jump the starter and it turns the engine over and it will start but only for a few seconds. i have had the car for 4 years with only having to replace the TPS and lower manafold gasket and now this problem has me stumped.
so if anybody could help me that would be apreciated

Maybe try a different key. I had same problem. There is a resistor embedded in the key which acts as security device. These contacts wear down over time and will prevent the car from starting. I used my backup key and starts every time now. Then again, it may be something more complicated. But it's worth a shot.

The service manual says the "SECURITY" lamp should illuminate for 5 seconds when the ignition is first turned on, if they system is OK. If it stays on or flashes, there is a problem.

Also, if the system senses an incorrect key resistance when attempting to start, starting (including fuel) is disabled for about 3 minutes.

A defective Tranmission Position Switch (TPS) or adjustment, could also prevent starting.

On my 95 Cutlass Supreme, the back-up lights stayed ON when the car was OFF. I had to remove the fuse (and then my electric trunk release wouldn't work). After a bit, I put the fuse back in and now the back-up lights didn't come on anymore. I assume it's the TPS or wiring. I haven't replaced the TPS yet!

A defective Tranmission Position Switch (TPS) or adjustment, could also prevent starting.

On my 95 Cutlass Supreme, the back-up lights stayed ON when the car was OFF. I had to remove the fuse (and then my electric trunk release wouldn't work). After a bit, I put the fuse back in and now the back-up lights didn't come on anymore. I assume it's the TPS or wiring. I haven't replaced the TPS yet!

TPS is throtle position sensor.
YOu are thinking of the Park/Neutral safty switch.