A lot of the panel TVs (LED or plasma) have a motherboard/daughterboard that goes bad and leaves the unit unresponsive. I've had it happen to one TV and there are many others out there who experience the same thing. Thankfully the fix is usually easy and not too costly. You can look up your model and find the parts from a retailer and replace yourself (there are lots of How-To's dedicated to this on Youtube). You may want to open it up and look around for any burnt capacitors and locate exactly where the problem is as it could be something as simple as just soldering a new one in place which would be super cheap. If there is a problem with where the power comes in then be careful with it. Make sure it is unplugged before working on it and make sure any repairs to that area are clean and nothing is bridged that could cause a short.
When you say "flashes empty" is that the flashes on the charger? If it's blinking slowly on multiple batteries then it isn't charging them correctly. If something is showing up on the camera screen when you switch it on, then I think you can rule out the battery door as the problem. If I recall, the camera won't do anything if the door isn't shut properly. Look and make sure the contacts for the battery inside the camera's battery slot is clean and has no corrosion issues.