PHIL,
It could be a defective cable or cable crimp to your TV box. Try another cable first. I had a situation here with RFI from various sources getting into my ham radios. My antenna cables all ran through a rather expensive remote antenna switch just inside my house. I discovered (with an ohmmeter) that one of the switch ports had a one ohm resistance in it's shield connection to the common port. In my case, the problem was a poor switch design, but a small resistance (less than an ohm) in a crimp or coax will let RF in or out. If I ran a KW the one ohm resistance could cause significant problems on TX. I have found that if run roughly ten turns of coax through a type 31 core you will usually get at least 10 db of attenuation on many of the HF bands. Other core materials are better for various bands and the optimum number of turns depends upon the band. If the problem is with the cables to the box and you can run 25 watts, 10 dB of attenuation should let you run 250 watts without problems. I have used several chokes in series for more attenuation, or stacking cores may be better in some situations. This is just one possibility, and other ideas such as ingress through the plastic box, etc. may be a more probable cause of your trouble. It is good that you "thresh holed" the problem, so say a toroid fix let you run 80 watts. You solved part of the problem, next you could try more cores, shielding, a new box, ingress through a power cable, etc. Often there is more than one source of RFI to or from a device. Many folks have more or better information. I am not an expert, just an "old guy" who has been doing too much ham radio for 66 years !! Rick KL7CW