Welcome and I think you raise some great questions.

I can't tell if you have cable or not but if you do, your old TV should work just fine -- while the power is on.

When the power is out, your battery powered TV may also work if it's hooked up to to cable. But it may not. It will depend on the scope of the outage and your cable set-up. A battery powered radio as a back-up for the TV is certainly worth considering if you don't have one already.

In the event of a extended outage as a work-around -- this may get a bit convoluted -- you could get a converter box and power it using:(1)a small generator, or (2) an inverter hooked up to your car. I'm sure others here will have even better ideas.

For Digital TVs, prices will continue to come down and the variety of offerings will continue to go up so sitting on your hands for a while may bring the solution you are looking for -- though that is hardly a good solution for you.