1987 Mustang GT stock gauge cluster not working... Need Help

I dunno for sure, but it certainly sounds like a bad voltage regulator on the back of the cluster. Though you did say you swapped clusters, the chances of having a bad regulator on both of them (providing the old one was salvage) is actually pretty high. The other thing I can suggest is that you make sure the ground circuits on the printed circuit board are intact and that there aren't any shorts or melted wires at your cluster's wiring harnesses. If you have a volt meter, check the respective wires for current.

This is a wiring diagram for your 87 cluster wire harnesses, it'll tell you what pin does what, and will help you greatly:

http://diagrams.hissind.com/?p=257

Looking at that diagram I'd definitely check the first harness, pin/wire #2. That's wire is the ground for that harness. The reason I say check that particular harness is that all the stuff you mentioned that has gone bad is on that one harness.