If you repair it, the TV may work for awhile, but they really need to be able to test the panel and yes, it is possible, but it's not as easy for a mobile technician unless they have the proper equipment. Even if they get it to work, the service warranty isn't going to be very long and you can't buy a longer warranty for service, only on new TVs.
The one time it kind of makes sense to replace the boards is if you know how to do it and you get a great price on the parts and you don't consider your time as a cost (maybe you look at it as a learning experience, which does have some value, if you want to think of it in that way). When you're paying someone else, you're not getting a great price.
I would look for a new TV and compare the price of the repair to a new one, then think in terms of "What if it cacks in six months- was it worth repairing?".