Hi ComputerWiz,
Well, the Kaspersky ended up finding the same thing at the end as it did in the very beginning of the scan: 5 infected files and 1 virus. Unfortunately, I was unable to clean ANY OF THEM. I could not check the boxes to remove the junk. I did, however, save a log of the virus info, and I found them deep in my documents and settings subdirectories. I already deleted Documents and Settings\Vero\jpi_cache\jar\1.0\arczip-28368554-336e44e5.zip. They are so old and have been in my computer since July or September of last year! I can't see how these items have suddenly started to cause problems. I believe that all the objects were from the same zipped file. They all start with the same long chain of numbers and letters: Documents and Settings\Vero\jpi_cache\jar\1.0\arczip-28368554-336e44e5.zip, then some have the extra ending: /web.exe, web.exe/data0005, web.exe/data0006, and web.exe/data0007. These were all called: Infected: Trojan-Clicker.Win32.Small.hn, except for this one: Documents and Settings\Vero\jpi_cache\jar\1.0\arczip-28368554-336e44e5.zip. This one was called ZIP: infected - 4, if that's a name.
This is very frustrating, as I still can't remove the partial file called Java 2 RE SE1.4.2_04. The Dial-a-Fix didn't do anything to remove it. I've never had so many problems related to Java.
Here is the Kaspersky file info, since my computer is not letting me attach a text file:
Infected Object Name / Virus Name / Last Action
C:\Documents and Settings\Vero\.jpi_cache\jar\1.0\arc.zip-28e68554-336e44e5.zip/web.exe/data0005 Infected: Trojan-Clicker.Win32.Small.hn skipped
C:\Documents and Settings\Vero\.jpi_cache\jar\1.0\arc.zip-28e68554-336e44e5.zip/web.exe/data0006 Infected: Trojan-Clicker.Win32.Small.hn skipped
C:\Documents and Settings\Vero\.jpi_cache\jar\1.0\arc.zip-28e68554-336e44e5.zip/web.exe/data0007 Infected: Trojan-Clicker.Win32.Small.hn skipped
C:\Documents and Settings\Vero\.jpi_cache\jar\1.0\arc.zip-28e68554-336e44e5.zip/web.exe Infected: Trojan-Clicker.Win32.Small.hn skipped
C:\Documents and Settings\Vero\.jpi_cache\jar\1.0\arc.zip-28e68554-336e44e5.zip ZIP: infected - 4 skipped
Thanks, Armo, for the firewall recommendations. Pop in anytime you want!

I had heard good things about the Kerio personal firewall from the WXP News guys. It's good to have someone else recommend them, as Kerio was also a sponsor of their newsletter.
I think my next step will be to run a Panda online scan, and maybe a Symantec scan online, as well. I've run many virus scans since these items were put on my computer, but no other AV has ever found these, which leads me to believe that they can't be causing all the problems I'm experiencing now. There has to be something else, right?