If you can, back up all your files--I had the same flurry of messages and it turned out to be either the hard drive or the motherboard...sigh...I've had enough failures lately, too, so I can't remember which it turned out to be that time.
Regardless, if it's your hard drive, when it crashes you can replace the hardware but all your data will be lost. And if it's your motherboard, it might be just as cheap to get an entirely new machine as it is to replace a motherboard. So you'll want your data backed up before it crashes so you can put it out on the new machine.
I sure hope it's not the motherboard--hard drives are cheaper and easier to replace!
Just a thought--I've had similar memory messages when my CD drive was failing. When you get the BSOD, are you trying to read or write to a CD or a DVD?