I am absolutely THRILLED for you!!!!! I don't mind telling you I was really, really worried that all would become one nightmare after another.

I enabled Windows to download their updates automatically as to not fall this far behind again.
A VERY good idea for you.
my computer literacy isn't going to win me any contests
But look how much you have learned with this problem! See, it really isn't so hard if you take your time, do research and follow instructions.

YOU DID IT! I am so pleased! Pat yourself on the back!

The newest java version is Version 6 Update 2. Check in Add/Remove and you should see other versions there, UNINSTALL all of them first. I know your logs showed at least one way out of date version on the computer. There could be others listed there so be sure to uninstall all of them.

Then go here
to download this latest version. I always recommend the manual install.
Once you have downloaded the latest version then close out your browser and install the new version of java.
Once the install is complete then go here
to verify that the install worked.

THEN, go to this sticky PROTECT YOURSELF FROM MALWARE: Tools & Tips

Be sure to use a Firewall. Either the built in Windows firewall or one of those PP has on the sticky above. Remember though, JUST ONE firewall and JUST ONE anti-virus program.
Download and install SpyBot S & D. Update it and be sure to use the Immunize feature. DON'T use the TeaTimer portion of the program.

I would also recommend using AdAwareSE and most of all be sure to download, install, update and enable SpywareBlaster. This program is a MUST. It doesn't run in the background but offers superb protection against spyware, malware, tracking cookies and has a Restricted Sites portion that should be used also.. It works with both IE and Firefox, which I also believe you were using, continue to use Firefox it is much more secure than IE though of course IE must be used for Windows Updates.
Please keep us posted on how all is working. Can't tell you how pleased that all worked out!!!!

P.S. Just noticed this in your update.....
I'm going to contact Norton to see about getting NAV 2008.
If you don't have an anti-virus program on the computer then this should be priority #1.
I use Norton, have for years without difficulty, though I know some folks don't care for it...I do. If you want to go with a new Norton that is fine, especially since you are comfortable with it, but just go for the Anti-virus program. Don't go with their Norton Internet Security Suite. I only say this because I have seen so many have problems with it. Another option you do have is using one of the Free Anti-virus programs that PP has on his sticky. I have installed AVG on many computers I have worked on for friends and family and it is easy to use and they all have had very good luck with it. But any of those PP recommends are very good and offer extremely good protection. The choice is yours, just get one on there ASAP if you don't have one installed yet.