In my experience there are usually three things that can fix this issue.
1. Reseat the memory (Also it could be bad memory)
2. Replace the power supply.
3. It's an issue with the motherboard and it will be replaced.
Now, if you only need to get files off and you don't care to fix the computer, buy an external hard drive caddy. They can be had for $20 or so and connect via usb. You just take your hard drive out and sit it in the caddy. It basically functions like an external hard drive at that point.