Thank you so much for all your help and sticking with me yesterday. I was able to get to the updates page for Windows ME using the first link you posted in that message about Win98. So I am going to post the fix again here, changing 98 to ME as it worked perfectly following Nimrod's exact instructions to the letter. I found 25 criticial updates, and 44 optional ones. However Microsoft's updates page did note that ME and 98 would no longer be getting any additional updates, but at least the first 25 critical ones are still available. However to get to them, it's quite a challenge. Here is the fix:
1: First, I believe you must have IE6.
2: Delete all temporary internet files by right-clicking your hard drive, selecting 'Properties', and clicking the 'Disk Cleanup' button.
3: Perform a repair on Internet Explorer by going to your Control Panel, selecting Add/Remove programs, and selecting Microsoft Internet Explorer. There will be an extra option to repair your IE6 install.
4: Once you have done this, reboot, and immediately go to Windows Update.
After doing all this, I finally got the update site to properly recognize my OS as Windows ME. As an additional note, once I had done some other browsing and downloads, the update site once again thought I had a Mac, so I had to go through it all over again to get the last few updates I needed.
That's it. Thank you so much. I feel much more protected now. :-)