My pc recognizes the device, but the screen won't turn on?

I was using my iPhone 4 on ios 7.0.4 listening to music. The phone randomly turned off. The phone now won't turn on however the PC recognizes it as in DFU mode. It wouldn't restore, and an apple genius said that they could not fix it. When I got home I was

successful in updating it to the newest ios and the screen turned on. I set the phone down for 5 minutes and it shut off to the same state.

I know the phone obviously works, I just dont know how to fix my specific problem. It was jailbroken when it shut off the first time.

I have attempted to restore the phone on multiple computers, both mac and PC. I've tried force booting the device and attempted to use programs to do a fix recovery.