In a proper 3 wire power plug install, the "death cap" should be disconnected and thrown away, and the "ground switch" should be disconnected completely inside the amp. Additionally, on older amps they had the fuse on the neutral side and the power switch on the hot side. These should both be moved to the hot side with the fuse first, and then the switch, and then from there it should connect to one of the power transformer primary wires, and the neutral side should go directly to the other transformer primary wire. So it sounds like that person did not install the power cord correctly.
Hum can be caused by grounding problems, but if the grounding was not changed in the amp, then the problem is probably something else. It can also be caused by bad electrolytic caps, and bad filter and bypass caps can cause other things too...low power, intemittant issues, messy electrolyte leaking inside the amp, etc. If these filter and bypass caps are original, then that would be the most likely place to start. Have these caps replaced, preferably with some new ones that will be able to handle today's wall voltages instead of the can. (search for it, there are many posts relating to this)
Greg