No picture or sound on new zenith

It sounds like the set is going into high voltage shutdown, a safety feature which shuts off the set if the power to the picture tube gets too high. Once the set shuts down thus way, you can't turn it back on until you unplug it and plug it back in again.

There's nothing I can suggest that you can do to stop this. This might be due to high power line voltage in the house. There may be a problem in the set and the shutdown is doing its job. Or there may be parts that are defective or out of adjustment that are causing false shutdown. Any work on a TV that involves its protection circuitry is best done by a qualified technician.

If the TV is new enough it might still have a warranty. Check into that first, then look for a servicer in your area and get an estimate.