If a TV, or any electronic device, won't turn on at all, it can often be a problem with the power supply to the unit. With the Polaroid FLM-323B TV it sounds as though this may be a fairly common problem, as research into this particular model shows that quite a few other people have had a similar issue.
That's the bad news. The good news is this means others have researched the problem. The following YouTube video suggests the issue is really straightforward to fix, and shows you how replacing the diode in position z9 returns power to the TV (signalled by the blue light coming back on at the front of the TV).
The only other thing I would say is to weigh up spending time and money on repairs versus buying a new TV. The price of TVs has dropped dramatically in recent years, and the benefit of a new device is that they come with a warranty if you have any problems in the future.