Programs stop suddenly

This may not be necessary to say, but I'm very new to Linux & Ubuntu. But I've been wanting to try it out, and I had an old hard drive lying around that's never been used, so I figured I'd install it and give Ubuntu a try.

The install went less than smoothly, but I finally got it up and running. It took several attempts to install updated packages and drivers. I'd start it downloading, go do something else, and come back to find the login screen. Not sure why it logged me out, but start it again, and the same thing happens. It would make a bit of progress each time, though, so I just kept trying until it was finished, hoping that would magically fix everything (I realize that was naive). Once it finished, I reboot, and just start playing around with things, trying out the games of course, trying to access a network drive where all my media is stored with no luck, surfing the web with Firefox, etc...

Weird thing is, every so often, whatever program I'm using will just suddenly close. No warning, no error message, nothing. Usually I can start it up again ok, but not always. Sometimes it will just open a window then immediately close again. And every now and then, everything just freezes and I can't do anything except shut the whole thing down.

As for the system this is installed on:
Compaq Presario SR1910NX
AMD Sempron 3200+
Onboard Graphics & Radeon X550XTX (the screen kept flickering using the Radeon, so I went back to the onboard graphics - NVIDIA GeForce 6150 LE)
Came with 512 megs ram, I added 2 more gigs - 2.5 gigs total
Ubuntu is installed on a 40 gig Seagate Barracuda ATA IV, and WinXP Pro is installed on the "stock" 120 gig HD, also a Seagate Barracuda

Any thoughts? I'd appreciate any suggestions you might have.