If you have an administrative account, you can browse to \IP\c$ and get to the Admin share of the C drive.
You could also connect with WMI and list / remove files by script, but I don't know any program that will present it neatly. DameWare Remote Support free trial might.
If you can install some things, but RDP is broken, then PSExec from SysInternals will let you run a command prompt on a remote computer. It does need Admin rights, and to push a small service file though.
GenControl will push-install a small VNC server which sometimes works if RDP won't. Authenticate by browsing to \IP\ipc$ and entering a username/password first, then try to connect with Gen Control.
These often help me - it depends how much access you have (permissions and firewall open ports/allowed kinds of connections), how much disk space there is, and precisely what is broken.