There are a few reasons why this might be happening.
You are right - Home does not have a way to adjust Group Policy with a Group Policy Editor, but it the registry still has all the pieces to manipulate even though it must be done through regedit instead of letting the Group Policy Editor manipulate the registry for you.
The .reg file you downloaded and ran addresses one possible reason by adjusting a value in HKCU, but there are other things to check. Remember, malware is sneaky and likes hide and seek.
If you preform a Google seach for: xp desktop tab missing
You will get some hits that include the fix you downloaded, and a couple other registry values that you can check. One more in HKCU and one in HKLM, and some others that I did not try. Some involve using the Group Policy Editor (which you don't have anyway) so skip those!
Reinstallation (or System Restore - which is not a time machine) is a little drastic... Too many easy things to check.
The last time I responded with detailed registry adjustments here, I was advised to please not to do that again, which I understand
Let us know what you find.
Edited by joseibarra, 04 June 2009 - 06:05 AM.