I have Windows ME loaded on my home PC. Its a Compaq Presario with P4 etc, 128 RAM etc. I also have a cable modem attached to it
Lately I have noticed something very funny. Whenever I take my pointer near the icons on the desktop they all do quick muical chairs, change places with each other and I have to really quick to click the icon I want.
Any reasons for this?
I do not want to make Gates any richer by upgrading to XP so thats out.
You may have a trojan on your computer.
You need to go a a virus site (http://housecall.antivirus.com) and scan your hard disk. It also would be a good idea to get some antitrojan software. I use Ants (A New Trojan Scanner). It’ll get to the root of the matter with a port scan (the downside is that much of it is in German, so you need to be able to translate (http://babelfish.altavista.com does an adequate job). There are also some cleaning tools at Hackfix. And here is a page with some cleaners.
You should also install a firewall like ZoneAlarm. No one with a cable modem should run without a firewall – ever.
There are some other viruses that do this as well (not just trojans), like W32.Magistr, which has some nasty payloads. Norton Anti-Virus is your friend. 
http://www.mcafee.com/ has an always uptodate ONLINE virus scanner. They just added lots of popups though, nuts.