Importance of Grounded Power?

I recently got an old AlphaServer 4/275, and it worked for a while, and then after I moved into another room, and it stopped working. I only have one or two grounded outlets in my apartment, so I had to hook it to a non-grounded one (via a surge protector, plugged in with a grounding adaptor). I'm not sure if it's coincidence, but that appeared to kill the AlphaServer (the power supply, to be precise). Is it technically possible for non-grounded power to be able to kill a system? In general, what type of hardware will require real grounded power to function? I have a whole slew of PC's, for example, using non-grounded power outlets without a hitch, so is this only going to be a problem for industrial equipment, like AlphaServers? Also does anyone know where I could get an AlphaServer 4/275 power supply for cheap? Thanks, Terry