I would try once more to install in safe mode, with networking if you do not have the SP2 installer. Or try SP3 in safe mode, skipping SP2, which you do not need since you have SP1 installed
Or Try this if that fails >>
You receive an error message when you try to install Windows XP Service Pack 2 or Windows Server 2003 Service Pack 1: "Access is denied"
And if that fails as well, here is a similar fix, but users state a different key/keys to change
Solved: XP Service Pack 2 Install - Access Denied - Tech Support Guy Forums
Also fix is here, midway thru there is a link to a thread and how to make a command file from the text
Service Pack 2 “Access Denied” error message at Random Fix - Computer Help