1997 Chevy Lumina that I can't get started.I can turn on the key, all the lights are on, but when I try to engage the starter it does nothing and the headlights blink off.  I can jump  the starter with a screwdriver and the car will start but the engine will immediately shuts off.  I'm thinking it's a key chip code problem, but we have tried two different keys.

I tried to rent a code reader but they told me the car needed to be running for it to read codes. That does not sound right to me. Please help direct me in the right direction as this is the wife's car and it's been down a couple of weeks. Any help is greatly appreciated.

Sounds like a theft issue. That system has a common problem with the Passkey ignition key cylinder. There are two small wires that attach to the cylinder and read the key resistor chip. Those wires break. Just trying a different key wont help, it needs to be the correct security number. That number can be read from a tool at the dealer. The way to check if the passkey ignition cylinder is bad, is to go under the dash and check the resistance of the 2
white wires with the key in the ignition. Use an ohm meter to check the resistance of those wires. If an open circuit, then the cylinder will need to be replaced, and a new key cut to match the cylinder that had the same resistor chip value. Not sure how knowledgeable you are with cars, so you may want to take to a repair shop.