Computer restarts while trying to install Avast

Hi, I recently purchased a Dell Optiplex 755. I performed a clean install of Windows 7 professional, 64-bit, for my parents to use. I tried to install Avast, and at a point in the installation, the computer restarted. The computer turned back on, and running the setup again, it installed correctly, without rebooting. BUT, when I put it to sleep, and tried to wake it up, and it just restarted.

I was having the restart from sleep problem before, but after making a few tweeks to the power options, I fixed that problem. I am at wits end on this; I've never had a computer fight me this hard! Thanks for any help.

Hi andrew129260, I did try and install AVG. Everything worked like it should; it installed correctly, and did not cause a restart. I believe it is a problem with Avast, and not my PC, but now I'm having another problem.

While I was surfing the net on it, it just randomly restarted. No warning whatsoever, no loud beep; NOTHING! Just restarted. What could have caused this? Is this STILL software related, or is it hardware? Thanks for any help.

Hi andrew129260, thanks for your reply. I mostly suspected hardware, but was hoping it wasn't. I am very comfortable working inside a pc; not a big deal. I don't by chance have a psu tester; I will double check the connections to the board and rest of the hardware components.

I also tested the memory using memtest86; i did 3 complete passes, and it was OK. I was originally suspecting mobo, but psu makes sense as well. I hate even suggesting this, but if i took it to a local computer shop, could they test the psu for me? Thanks for helping.