Do you not want to (or are not allowed to) install any software at all on your Windows machine? Is that the issue?
If you can install something on the Windows machine, I would thoroughly recommend the
Cygwin environment, which includes an excellent version of SSH. Cygwin optionally includes an X server, though I've never used it.
Also, there is a separate X server for Windows that I haven't used either, but I hear it's good,
Xming.
But if you really can't install any software at all, then the only option you have is to use a web browser (even that horrible Internet Explorer) to access web apps running on the Linux box.
I thought I remembered that
TightVNC has a mode that runs in a browser, but I don't find any reference to it now.
There's also
FreeNX and other NoMachine software that you could check out. I don't know much about it.
Hi 
Linear Mode
