It shutting off after 10-15 minutes sounds to me like a heat problem caused
by the fan not working and/or dust preventing the CPU from being cooled
properly. Do a Google search and see if you can find instructions on
disassembling the laptop and checking the fan and dust level and blowing it
out. Several years ago I had a fan lock-up on me, I sure some use the
cheapest bearings they can find because 2 years out its your problem, and
had to replace it.

I had an ACER netbook system board go out on me last summer. The replacement
was more than the computer was worth. Fortunately I found instructions on
Google on how to disassemble it. I removed the HD and placed it in a Kingwin
SATA external enclosure so all the goodies we are suppose to keep backed up
and don't was recovered.