It indeed doesn't sound good when your system produced a crititcal error when you are viewing/downloading data through a plugin in the web browser. It's beginning to look like something in your chipset isn't working right. The chipset on your mainboard regulates all communications between processor, memory and any attached hardware. There are a couple of tests available to see if this is the case.
You can do a throrough scan for bad sectors on your hard drive by manually booting into MS-DOS mode, and running scandisk. That first will do the same quick scan like it does as part from the windows setup, but then you can instruct it to do a full surface scan. Depending on the size and speed of your hard drive, this may take a couple of hours. But when there is a problem somewhere in your hard disk subsystem, it will most likely be found.
If scandisk doesn't turn up anything, it's time to thoroughly test your memory chips. You can do this with a little test program, which you can download here:
http://www.memtest86.com/. You need to put it on a floppy disk, and have it in your floppy drive while you reboot. If your memory has any problems, this will find it.
A further test for system problems can be found here:
http://www.computerbase.de/downloads/software/systemueberwachung/prime95/. Technically, it will calculate prime numbers (hence the name

), but is does it in such a way that it also stress tests your mainboard hardware (chipset/memory/processor). If anything in this combination is wrong, Prime95 will most likely find it.
Finally you can download 3DMark from here
http://www.futuremark.com/. It's really a 3D benchmarking program, but it will thoroughly stress test the north bridge of your chipset, which deals with communications to your video board, processor, memory and your hard drive.
Jan Peter