Thats exactly what happened to mine. I was able to play for a few minutes or even at one stage 2 hours before it went of and YLOD for a while. I kept on playing and shit they it just died all together. I rang Sony and they said my warrenty was out so i would have to pay alot of cash to get it fixed. In the end i just bought 1 of someone i knew for really cheap. I know how you feel not wanting to open it up but unless you have the money mate thats what i suggest you do.
Heres a guide to fixing your ps3:
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