If you aren't crashing, it sounds like you are overheating your computer. If your computer is a desktop, take a can of air duster to the insides, that will help with overheating issues. Also, always run your laptop on a hard surface, such as wood, glass, or hard plastic. Soft fabrics can prevent proper air flow and lead to overheating.
EDIT: Totally missed the line where you said "And now it won't power up", despite the title of the thread. Refer to celestar's post.