Assuming you hear no clunk or whirring noise, it sounds like just a wire somewhere. I don't think these cars have the computer involved in between the start signal from the key to the solenoid.
Check the ground straps, there's three IIRC. Check the starter motor main power lead, if you can reach it. Make sure it has 12V. Starter is grounded by being bolted to the motor, so the motor needs it's ground straps to start.
If you can reach it, you can try to apply 12V to the solenoid start terminal (with key off). That should crank the engine over. Make sure it's in neutral, and parking brake on obviously!
If it cranks, the problem is signal to the starter solenoid from the car. Check wire harnesses, etc. You can also check for 12v on the solenoid lead while the key is turned to start, to see if the car is sending start signal to the solenoid.