Join Date: Dec 2010
Location: Homestead, Florida
While "banging on the fuse box" is a clue, there are many things that could be causing the issue that you have. This is not a situation that has come up before, so I doubt that anyone can pinpoint, with any accuracy, the location of the defect.
Using the label on the inside of the fuse box lid, locate, remove, and check the three fuses that affect the PCM. They are #20, #25, and #30. Check to make sure that the fuses seat securely in the sockets and don't feel loose.
Find the "Powertrain" relay, #56, and check it also. You could swap it with one of the other relays that have similar markings. I'm not sure which, maybe the "Horn" relay, #55.
It doesn't sound like it would be a "short", but something appears to be not making proper contact.