Remotely connect to computer where I don't have admin access on
Assuming the PC is logged in to a user account you can access occasionally, you can run Real VNC Server in usermode. it does not use the MS authentication so there is no requirement for admin, beyond those that you the actions you take in XP require.
VNC authentication is weak and its traffic is unencrypted though, so you only want to use it between PCs on the same LAN. It is not safe to use over the internet unless you tunnel it via ssh or another tunneling encryption protocol.
Another option to try is UltraVNC, which does not require installation.