Computer randomly shuts itself down.

All laptops have a standard warranty of something between 1~3 years -- check your manual to know for sure.

If you can't send it in for repairs, then you might need to take the cover off and blow out the dust with a compressed air can. Check if your manual shows you how to do this "heatsink/fan cleaning". If it doesn't, then search Google for a disassemly guide for your model. Just be careful when you do that. >.o