Acer Laptop runs but shuts off suddenly

I've had an Acer 6930 laptop for almost a year. I had the two Usb ports go bad on the right side and got a BSOD stop error while burning a Dvd. Sent to Temple repair. They replaced main board and hard drive (unfortunately.) Computer runs now but turns off suddenly for no reason after 2 - 10 minutes. I have tried only on cord or battery (both battery and cord work fine.) Computer will even turn off just running BIOS or in safe mode.

I'm thinking from what I've read on this site possibly three problems:
1. Power button is shuttting down computer. I had to power off the computer a lot by holding down power button. Computer failed to go into sleep mode often. It would turn off the screen - leaving me no other option.
2. When Temple put computer together, some part not hooked up properly
3. Overheating problem - computer always ran hot especially in the lower left corner of the keyboard