|The start button is a long shot, but the PSU is a possibility. When's the last time you cleaned the inside of the case?|
"do I replace it with the same power which is 350 or do I go up?"
That depends on your system specs & what your future plans are. The system will only use as much power as it needs, so if you went with a higher wattage unit, you wouldn't be wasting electricity. It'd be better to get a 500W unit (for example) & have a 150W safety factor, than have a 350W unit running close to max capacity.
"And that's the fishing line, because Sharkboy said so!"