The fact that it runs for 5 seconds at start up is the clue that psfred is correct (as is usually the case) and also the thread you found says the same thing. I do not have a schematic for this car so cannot speak authoratatively, however assuming that the ignition control module does send a signal to the fuel pump relay, then if you can determine what "signal" it is supposed to send, you can put a meter or oscilliscope onto that wire and look for the signal. That would tell you where the trouble. I have a scope in my closet don't you?... Well on a college campus you should be able to find a scope, unless it's liberal arts. And try to get the scope operator (someone who knows how to use it) or you might not get any use out of it. Bigger problem might be figuring out what to look for: A square wave, high voltage, low voltage... Saving money isn't always easy but you can learn a lot.

Mike

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1998 C230 330,000 miles (currently dead of second failed EIS, yours will fail too, turning you into the dealer's personal human cash machine)
1988 F150 144,000 miles (leaks all the colors of the rainbow)
Previous stars: 1981 Brava 210,000 miles, 1978 128 150,000 miles, 1977 B200 Van 175,000 miles, 1972 Vega (great, if rusty, car), 1972 Celica, 1986.5 Supra