Bad Power supply? Unsafe ground wire?

Computer sounds like it's going to shut off but doesn't? Other times it completely loses power. I've been using a 3pin to 2pin adapter as a ground since the wall socket isn't grounded. Also when I touch the metal of my computer case I get a slight shock. I'm going to assume the computer is not grounded correctly if I'm getting shocked?

1. Is this bad for my computer?
2. Could this be causing flaky power issues if it's not grounded properly?

 
1 if damage hasn't already happened you should shut it off and unplug it before it does
2 yes but as you said the wall socket itself inst grounded so the psu couldn't possibly ground itself properly