Focused EMP backed up by super extra heavy shielding, or components not very susceptible to EMP.
There's more than one way to generate that type of interference, FYI, which is one reason the FCC has so many regulations concerning devices, just so ya know.
One sure-fire, but probably illegal, way to wax the other bots would be by microwave emitter, not the chintzy kind in a mini microwave neither, the high-end blaster used in phone towers - you could most certainly FRY the guts of another bot with one of those... but you might bag some of the studio audience too, tho in my opinion, that's THEIR problem, heh.
Another good weapon, tho I consider it a bit fragile for the purpose, would be the "Heat Ray" I built for science class one year after reading War of the Worlds.
It's not a lazer, but a million candlepower dive light focused through a tube of stacked convex lenses, the same principle as using a magnifying glass to fry ants, but on a somewhat larger scale.
Mosta the effective nastiness I would arm a robot with, however, would be regarded with shock and horror even prior to the institution of those rules, just cause they're so abysmally nasty.
Would a twin barrel epoxy sprayer be classed as a "projectile weapon" ? probably. (and a solvent sprayer in our robot to keep it's own motive power system clear..)
70mm x 150mm shaped charge, impact-detonated rocket launcher with an 18 round gravity feed clip ? that'd be right out, too, wouldn't it ?
The one thing I could contribute to such a bot that might pass would be a sandwich style layered armor plate of surprising effectiveness, but that's one secret imma keep to myself.
The really pyscho thing is that I have, in my youth, BUILT most of the widgets above, with the exception of the microwave emitter..
Are thermal lances forbidden too ? if one could get past the fragility problems of such a device, they could make awful short work of any bot that came near it, not to mention chop the obstacles into fodder too !
(I've never seen the show, mind...)