rohaninabout,
UltraVNC is maybe not the best solution and here is why.
If you are forwarding a port from the router to the PC that's running VNC server, as it sounds like you are, then anyone on the internet who attempts a VNC connection to that static IP address would get forwarded to the PC and get a username/password prompt. At that point a password cracker could get someone in and gain control of the system.
You mentioned Malware removal in your post, this also could be a point of entry if all the infections were not fully removed. Upon reboot the system could become reinfected and allow access through a trojan or become part of a bot-net.
Both of these could explain the slow down or the desktop problem.

