A buddy of mine recently picked up a new boat after the "old" one started taking in a bunch of water while the engine was running his last time out on the lake. He said that they were motoring across the lake and noticed water coming out of the engine compartment so they took the cover off and saw water coming in. When the engine was off, no water would come in... but as soon as he started it back up it starting coming in again.

He was able to drain it with the motor off and then fly back to the ramp... and he spoke with someone that said it would probably cost more than it's worth to fix it. The boat is otherwise in really good shape and it's already been replaced, so I can basically get it for free. My questions to you guys are, any idea what's wrong with it and how much it may cost to fix it??? The motor still runs well and has about 500 hours on it. Thanks!

If it's an inboard and only getting water when it's running, I would look at the water pump on the engine or check the hoses.  Might want to check the exhaust manifolds also.  They are water cooled and could have a leak in one of them, it's common for them to rust/corrode through.