You can find one most likely from an auto dismantler (junkyard) who pulls engines and stores them in racks. Please reply to us all and tell us why the mechanic is saying why you need a new one.
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A used one will do the trick, you can find them even this age in relatively good shape. Connectors are readily available to repair the old one but I can see the damage you have in my minds eye seeing the PCM is under the battery IIRC, that connector would be a real bugger to swap and repair wires close to the connector.
This is a 06, check the part# on yours and one of these, it will probably fit the 05, search for an 05 on that site also. A junkyard you can take your own stuff off is your best bet.
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Your car probably uses a "E40" style PCM with the Delphi Micro Pack connectors, Not the easiest to field repair (As in removing pins & swapping wires)
The good thing is....These connectors have a plastic shield over them & unless the mice ate through the cover then ate some wires close to where they terminate?.....This should be easily repairable buy removing the shield/s giving the mechanic some wire length to work with.
had a 05 gt. had the normal gm problems, but overall a good car. had 247k miles when i traded it. transmission was on its last leg. service the transmission every 30k.