Two weeks ago I went through more or less this same experience with a 5 year old black Macbook computer. I spent about a month trying to troubleshoot my home wi-fi network because I kept losing the signal. Long story short, it turned out to be a failing wi-fi card in the computer that worked intermittently until it failed completely.
I took it to the only authorized Mac dealer in town (where I've been a long time customer) and the owner told me that it would cost close to $200 to replace the card (it would be a used or refurbished card) and even then it might turn out to be the logic board and so on and so forth and it really wasn't worth it to put money into such an old machine, etc., etc., etc. Then he tried to sell me a new Macbook Pro.
Well, for one thing this laptop does everything I need in a laptop for the time being as I do all my computer "heavy lifting" on two powerful desktop machines in my office. For another thing, this would not be the ideal time for me to blow 1500 bucks or more on a new computer that I primarily use to surf the internet, show jobs to clients and do basic word processing on. Finally, I've previously installed a much larger, higher speed hard drive in this machine and maxed out the amount of ram it will accept, so along with all the latest software updates this little old laptop performs pretty admirably.
So I went home to weigh my options and found a reliable dealer on eBay that offered a used 802.11n card (which would be an upgrade from my 802.11g card) for 26 bucks delivered, with a 12 month warranty.
Well, taking the computer apart was a bit of a challenge because this generation of Macbooks has a bit of a Chinese puzzle like design (For example, looking at a row of ten identical screws you need to remove screws number 2,4,7 and 9) but all in all not too bad and the web site
iFix-it was a great help.
In the end my computer is fully repaired and upgraded to the 802.11n protocol for 26 dollars total and I am entirely delighted and even feeling a little smug about how the whole thing worked out.
Obviously, risking 26 dollars is different than 200 but if you can find a source for the lamp you need at a good price it could well be worth the risk.
When I've told this story to a few people I know I've gotten the same weird comment. "He was just doing his job!" Really? To me having someone try to convince a customer that it is in his best interests to throw away a perfectly good computer and buy a new one is like taking your car to the dealership and having them tell you that you need a new water pump but, hey, the transmission or engine could go on you at any moment so it would be better to let us sell you a new car.
There seems to be a real disconnect in our society between all the popular talk about sustainability and the notion of living in a throw away consumer culture. I vote for trying to repair the TV if it really only needs a basic part and the rest of the unit is OK. Like snakebite says, find a reliable lamp dealer and if the price is good it should be worth the risk. You just might be pleasantly surprised with the results.