There was a problem with certain Radeon drivers a while back, where the driver caused the card to overheat and the game to reboot. This was not only a problem with our games, and it was something Radeon was supposed to have fixed several months ago. I'm wondering if they released newer drivers after that, which could have broken this again...? You might try the third party drivers at www.omegadrivers.net
-- they seem to work well for a lot of our customers.
Also - episodes 2 and 3 have performance problems because the version of the activation software we used on it had a memory leak. Episode 4 does not have the same memory leak. If you only started noticing problems with episode 3 (not 2), and the problems are continuing with episode 4, it's possible that this is a problem with something on the computer, not with the game. Are episodes 1 and 2 (which I presume played okay for you originally) still okay?
Just because the computer runs other adventure games well does not necessarily mean it will run Sam & Max well. The true test is whether it runs other 3D games well. That said, your Radeon 600 card should run the game.
But it might not run the game as well as it does Syberia or other adventure games. (Random reboots aren't normal, though, so I'd like to help you get to the bottom of it.)