Rear panel is live

Badger sounds right it may be an intermittent fault that has been resolved be moving it.

Static will build up on certain surfaces (shouldn't in a PC case as it should earth through the PSU). The only place an electric current can build up is in a capacitor or similar component. I wish you luck with your case, perhaps wear insulated gloves when changing cables or use a multimeter to see if it's safe before hand. Of course if you have any little-ones in the house I'd advise having it PAT tested, this shouldn't cost much for a single device.

If the case is hot to ground I would think the wall outlet is not functioning to ground. Do You have a three wire 110v system? If you do the case should drain via the plug and possibly (more than likely) trip a breaker (fuse). If you are not familiar with electric service the receptacle tester mentioned is a good tool to determine if your ground is working.