If you move the data hard drive into another PC where you can get administrator access, then you can gain access to the files and copy them to either another hard drive or you can reinstall XP on the system drive after moving things off it first..
First you need to turn off Simple File Sharing, you do this by opening an Explorer window and then
Tools>Folder Options>View and unticking Simple File Sharing
From there if you right click on the folder that you need to be able to access and choose Sharing and Security and the Security tab, then in the window that appears then click Advanced button.
Now click the Owner tab in the new window that appears this should then show a list of availible users that you can tell the computer to take the ownership of the folder. Choose the account that you are using at the moment, be it a User Admin account or the Admin account itself.
Also tick the "Replace owner on Subcontainers and objects" this will make you the owner for all of the files and folders contained within that folder.
Once this is done then you should be able to access all of the files and move them to another location.
You can also do this if you reinstall XP on a separate system partition and then if you cant access your files after that then you can use the above process to get your files back. This is as long as you have not "made the folder private".
I have used this on my own PC so I know it works definitely for Windows XP Professional, and I have been told that XP home also has the ability to disable Simple File Sharing and perform the above operations as well.
If you have any problems doing this then if you could post Screenshots so I can see what you mean.
Good Luck