Your post is too light on details. No words about the age, model and such of the machine. Some older machines never had the cover off and when we open it up the insides are filled with "dust bunnies". The heatsinks have fans on them which collects dust and bunny hair resulting in an overheated computer.
A simple cleaning can do wonders for these, but without details, its not clear if this is your issue.
My gateway has been freezing up. Then today I booted it up used it for awhile then powered down. As soon as it shut down I realized I forgot to do something so I tried to turn it back on. Nothing happened. No power. I tried it again a few hours later and it booted up fine. But when I shut it off and tried to bott it again nothing happened. Any help would be appreciated.