Went to a repair place, they asked for $300 to repair it. Wth???
Technician time costs the same for a $50 screen or a $5000 screen. Also, if you told them you'd worked on it before, they very likely gave you the "Please, don't bring it here, I don't want your bodge job" price. Can't tell over the phone if someone who has replaced the caps knows what they're doing or not, and half the time (if not more), that sort of thing creates as many problems as it might have solved.
But to diagnose and repair a TV with unknown issues, $300 doesn't seem at all unreasonable.
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As for the OP, as much as it pains me that we live in this world now, most modern electronics just aren't easy to repair. They're sold for a year, spare parts aren't available, and they're designed such that most of them will outlive the warranty period, at which point... whatever, not the manufacturer's problem anymore, except that if they last forever you probably won't buy another one. And if it doesn't last long enough, you probably won't buy that brand again.
You should be able to find a used 42" TV for not that much money locally, and even new, they're just not that expensive.
The question on the used logic boards is essentially, "Was this failure a one-off rare event, or a common failure?" If the failures of that TV at the 6 year mark are fairly common, you're right in that spending money on a used logic board won't get you much. On the other hand, if your TV just suffered one of those odd failures that happens, and it's not a common failure issue, then a used logic board should work fine.
However, if you're handy with an iron, I'd definitely suggest replacing any electrolytic capacitors you can find while you're in there.