You have the advantage that the owner of the equipment does want to fix it.
The usual list ... an external aerial for the TV should help. Don't run the TV and the computer off the same power point. As far as possible between the TV and the computer.
It might be the monitor, rather than the computer box (expecially since you have double filtering with the UPS). Monitors use switch-mode supplies too, and also have big currents in the video circuit. Try turning the monitor off (with the computer still running) to eliminate/prove that. If it's the monitor, you could try a filter on its power cord. (One simple power cord filter is a ferrite rod -- Dick Smith of Jaycars will still have them -- which you wrap the power cord around, close to the cabinet).
Since when has there been anything worth watching on television, anyway? ;< .