Due to the length of the run, this may be more complicated and expensive then you think...
Is there a reason you need the laptop at the soundboard?
If you havent bought the TV yet, I would consider a LCD projector. Prices have really dropped on them and they may even be comparable. You may be closer to your equipment and you can project on a retractable overhead screen which may be more visible then 50" and when rolled up less visible.
I see this setup used alot in churches. Many churches also project their weekend announcements/bulletin on it before service.
For the length of your run, using a VGA cable may be the best shot. Verify your TV/Monitor has one (almost all projectors have them) They sell very long VGA cables for overhead projectors. You may need a signal amplifier though if your run is too long. I am not sure offhand what the length limit is for the VGA specification. A composite video signal (yellow RCA jack) will give you the worst if not horrible picture quality. I wouldnt use it except as a last resort.. Many older laptops have a composite output.
If you stick with the TV/Monitor, I would suggest finding a older computer to dedicate to the monitor and just leave it sitting behind it, then you dont have to worry about finding and running a long video cable. If you have a wireless network or a wired network you can control the computer remotely by a program such as PC anywhere(dont think is free) or VNC (freeware). You can also do this with a network crossover cable. A local computer shop can make you one. The laptop would work well for this if it has a wireless card.
If you are using Powerpoint for the lyrics and such they make bluetooth remote's for use with Powerpoint. You can chage the slides and possibly load other presentations without touching the computer.
I have seen super micro pc's that can hang off the back of the monitor. They are about a inch thick and is about the same as half a laptop. They are designed to be used as electronic signboards and not much more, and i am guessing they are not very expensive.
Just a few random ideas.
