I've had 2x A600's die on me in the past 5 months, so I know what you're going through.

One of them was re-capped ny Amigakit. It worked for 3 hours, I left it on a game called Lethal Weapon... I went to eat my dinner and have a cuppa, I went back to the Amiga and it had frozen on the game, so I rebooted but all I got afterwards was a black screen.
So that game really was a Lethal Weapon.