Toshiba Laptop boots to sign in screen and then laptop shuts down

Last night I was playing JewelQuest 2 for hours on my laptop. I had just finished getting through another level and my computer just shut off like my house was having a power outage. Today I tried to boot it up and it came up to the login screen and then shut down. I tried it another time and it turns on and then shuts down. I am operating on AC power. Bottom of laptop was hot last night but I was venting it. Do you think it's my power supply? If so, does anyone know if I would have to order a replacement through Toshiba or if local Laptop businesses would carry parts for Toshiba's?
My Toshiba is a Satellite A15-S129 I've had it about 2 years.
If my toshiba is toast, is there a way to get what is on the hard drive off? I just bought a bunch of music from itunes and I would hate to lose it.
Thanks,
leema