cygpup,
The machine has some ROGUE process(s) / background programs running which are eating up available memory.
Download, install, update and run FREE edition of program below immediately in safe mode.
http://www.superantispyware.com/download.html
Someone is going to have to get the antivirus program running also.
Back up all important documents, pictures and items as a Clean Install of the operating system may be required.
Simply put, the machine has got a virus or Bot running on it.
Regards,
Rick P.

This must be clearly disk space not RAM. One cannot loose RAM. As a first fast and dirty fix I suggest to reduce (resize) the shadowstorage to e.g. 1GB. Here is a good description on how to do that.. Next you should post how big the total disk partiton (probably C:) is. Then you should think about getting an external device (USB stick or external disk) to offload some of the files. (this week, a 16GB USB stick is on sale for only $15.99). Finally, take the time to run WinDirStat (once you have reduced the shadowstorage and can download things) and take a snip of the numbers (not the color picture) and post that here so we can have a further look. Maybe there is something that does not belong there.

@Rick, I did it again. That happens to me all the time. I am really sorry, but it was a lot of work to put this post together. I'll save it for another day - lol.
@Cygpup, I am sorry. I did not fathom that this was an XP matter. Keep forgetting that XP is still around. I thought I could help. But in XP matters I am a null. You are in better hands with Rick.
BTW: the 16GB USB stick may still help in this case!

Ya, prices are really coming down. Last week there was also a 640GB Maxtor disk for $89. I find this stuff on this website. They are only a repository where all these companies post their deals. On the bottom of the page you can make a selection by subject.