My Gateway GT5654 desktop just quit in the middle

Based on my experience, the most probable cause of your problem is the RAM. Try Cleaning the RAM first by removing it from the slot, and rub the pins with a pencil eraser. As shown on the image below:

Then re-install it to the motherboard. If problem persist, you may need to replace your RAM.

Note: If you have two RAMs on your pc, might as well clean them both, and then test each RAM to find out if either one of them or both are busted.