Inverter help please.

Sound like a problem with the tv. Maybe internal short causing it to pull too much.

 

Typically, when you get a beeping/overdraw from the inverter (as in situ #1), the inverter's input voltage is too low. Like an engine off condition with partially drained batteries, at say 11.7 volts). Same with the larger inverter. Does the TV work if plugged into the inverter while the engine is running, at say 13.5v or better?

But I'm more inclined to believe that the TV is real "picky" about having regulated clean power (pure sine wave) to it, and since most inverters produce square/modified sine wave, that may be the problem. Pure sine wave inverters cost more, but power sensitive electronics much better.
But it's always possible the TV is faulty, and trying to pull too many volts/amps, compared to what either inverter can put out.

 

I've had problems with the switching power supplies provided by an appliance manufacturer being incompatible with an inverter. Inverters are just another form of switching power supply, and sometimes this stuff just doesn't play well together.

 

Yes, that was one thing that I forgot/left out. Sometimes it can be a capacitance issue, and you can nurse it by repeated power-up attempts.
I also had a TV that required that once, during an extended power outage, and running off a few deep-cycle batteries & an inverter.
Glad you got it to work, even if it's a "charge up that pacemaker" kinda method.