I have a Westinghouse Flatscreen that keeps shutting off automatically and sometimes won't even turn on. Is this a serious problem?

Maybe not hooked up properly, otherwise, yes, could be a serious problem. Sounds like an input problem, a converter problem. Do you have the right converter for the TV ?

Model number please.

When it shuts off, is there still sound and just the picture shutting off? Do you hear any relay click when you normally turn it on/off? If so, do you also hear the relay click when it turns itself off.

Does it automatically turn itself on?