You didn't mention the neutral safety switch.
If you have the service manual, look for the starter relay on the wiring diagram. There are four wires to it. You can split the system into four circuits there and test each one right from the relay socket to see which has the problem. I'm sorry that I can't get into the service manual sites but in general, you should find one terminal has 12 volts all the time and one should have 12 volts when the ignition switch is in the "crank" position. Those two terminals are on the same side, (at least that's how they are on a '98 model). The other two terminals should read continuity to ground. One reads through the starter solenoid on the starter, which we know is working because you're jumping it. The other one is either grounded directly or it goes to ground through the neutral safety switch. GM had different wiring versions for different years and models.
To boil it down, use a test light with the ground clip on the battery's negative terminal, then probe the four terminals in the relay socket. Identify the two terminals with 12 volts; one all the time and one with the ignition switch in "crank". Move the test light's ground clip to the battery's positive post, then probe the other two terminals. The test light should light up on both of them when it's in "park". Of the three that do not have 12 volts all the time, one of them should change when you shift out of park or neutral.
If all four circuits test okay, either there is a computer involved in the circuit or the terminals in the socket are stretched. For stretched terminals which do cause a lot of trouble, the system will often work if you push the relay sideways while a helper turns the ignition switch.
Sunday, October 28th, 2012 AT 1:59 AM