You never worked on a pile like this before. After the '94 models GM stopped allowing us to buy radio service manuals because they wanted to lock up all the repair business for their two grossly over-priced repair centers. Instead of spending way over $400.00 to get a cassette radio repaired, people like you installed aftermarket radios at a much lower cost. To combat that, they figured out a way to force unsuspecting owners into having to get the original radio fixed. They did that by building the Body Computer into the radio. There is no valid reason for doing that other than to make more money and is one of many reasons they ran out of repeat customers. Too many people said "never again".
A lot of the radios today don't have the common two power wires that you're used to finding. Instead of a memory 12 volts and a switched 12 volts, they use a main 12 volt feed and two "data buss" wires. The original radio needs a digital computer signal to turn on. A lot of cars also leave the accessory circuit live for a minute or two after the ignition switch is turned off to allow you to roll up the windows. Of course that means involving another unreliable computer but people don't care as long as they have their toys and gimmicks. That might be why your radio stays on. For your aftermarket radio you may need to run a new wire to the fuse box or to something else that turns on with the ignition switch.
GM started this nonsense with the Body Computer on some 2002 models, and I don't THINK it applies to your car yet, but if it does, you will have other systems that don't work once the radio is removed. The warning chime is one of them. If that is the case, you will have to buy a "radio relocation" kit. That will let you mount the original radio in the trunk so all the other systems work, and you just cut the speaker wires and run them to the new radio.
When you say it works when you connect some wires, I assume you mean it has proper sound too. If there is no sound, the car may have a remote amplifier. Many aftermarket radios today have line output jacks so you can use that same amp. If your radio only has speaker wires, you will need to bypass the amp if there is one.
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Thursday, November 1st, 2012 AT 6:47 AM