I haven't read anything about the ABC website causing problems. Watching videos may be more processor intensive and the machine may run a bit hotter, which might be enough to trigger a video problem that could have been there all along, but just hadn't manifested itself yet.
If you also get the blue stripes on an external display, that would indicate a problem with the graphics chip. If the video on the external display is fine, then the blue stripes could be a problem with your internal display rather than the chip.
If you get the stripes again, it might be a good time to run the extended version of the Apple Hardware Test, which is on Install Disc #1 of the gray discs that originally came with your computer. The AHT will test a lot of stuff, and if you get an error code, it will indicate a specific hardware problem. You can try Googling the error code and maybe find out what it is, but Apple is the keeper of error codes and would have to be the one to give you a definitive answer.
I can appreciate that you need to work on your paper and won't be able to mess with this right away. If your video goes away entirely, here is an article which might help you get it back again:
Troubleshooting: My computer displays no video
http://support.apple.com/kb/HT1573?viewlocale=en_US
This article will walk you through some resets which might help.
Also, sometimes problems are worse if the computer gets hot. If that seems to be the case, something like a chill mat might help until you have time for some serious troubleshooting. So would quitting any unnecessary applications while you are working on your paper.
Good luck!