What is wrong with my laptop... can it be fixed?

My laptop is admittedly a little old, however a problem occurs during any games or videos, even browser based ones, where the game will run smoothly half of the time, but this will be punctuated by tremendous burst of lag and low frame rates. My laptop is certainly not a gaming laptop (2gb ram, Dual core 1.9Ghz, ATI Mobility radeon X1200 integrated) but thes problems did not occur when I first got it. It also turns itself off at random intervals, especially when browsing the web. What could be wrong? Can it be fixed?