Overheated MBP now hangs at boot...

Friend of mine gave me a spare battery for my MBP which I recently fitted. I noticed the machine became hot during running with this fitted but thought nothing of it. After a long day at the office and my machine left alone I noticed the screen image corrupted and the machine so very hot. I shut it down, let it cool and tried to reboot. Now it has the gray screen with the timer and chimes. But the gray screen has vertical banding that looks like badly formed or corrupt tiles of graphical data. It lasts about a minute and the timer stops. That is as far as it gets. I can see it charges and I can also do a command-T and run the MBP as a hard drive and get all the data off no problem.

This is a mint, but old machine that I've hardly used, is it worth replacing the logic board, or even is it the logic board. I tried the external monitor and this doesn't register either.

Any thoughts??