Well, so many no's and not's. Hmm, if you're not going to use a professional repair service for diagnostics/fixing your computer but asking on the forum instead then I imagine you want to do some diagnistics on your own. I would try to rule out things like:
RAM - simply swap/replace the chips
Battery - pull it out to see if the machine still crashes
OS - by reinstalling or trying another hard disk because they fail quite often in my experience
I'm assuming you've tried booting it in safe mode, repairing disk permissions etc.?
And as for model number you can find it online searching by the serial number of your machine.