Overwhelmingly, it is probably cheaper to get a new TV. Especially if you can still get one on the tail-end of the Black Friday sales.
(I know someone who would go in there and do what's necessary with the (probable, from the sound of it) power component. He probably wouldn't replace an LCD backlight (and only entire LCD panels, where the size/make makes them practical to source as a component) and Plasma is an eclipsed technology with probably no easy component source. But an inverter/whatever unit might be gettable, or even repairable if upon examination it's a blown cap or similar. But you'd have to find such a chap of your own, locally, and if you had someone in mind already then you'd probably not be asking here.)
With various newtech, OLEDs over LCD for example, you probably be able to move at least a generation further on without breaking the bank, if not getting all the way up-to-date. The HDR of newer LCDs (cheating by backlight modulating) might not be too far off what you expect. Then there's the higher res/refresh/tuner options etc.
(It would probably be cheaper to get someone in there to fix it, with the right (unmercenary) soldering-iron-wallah, than a whole new item, but more fuss. And if you don't know them there's a chance they won't give you an honest "not economical to repair, mate" before doing and/or charging for a lot of expensive investigation/fixing.)