<Waggles Fingers> I wouldn't depend on that. For one thing, which version of Diagrom? Different versions test differently.
One thing to try if the games are for older Amigas (not AGA) - hold down both mouse buttons while starting and choose ECS or OCS rather than AGA.
Then try running the game again. If it cures it, no fault, it's just AGA trying to understand old games "hitting the metal",.
If these are AGA games, different story. They're not working for some hardware fault reason,
And no, points 2-3 not covered by testing the memory with a memory tester and finding all the chip RAM is fine. There are still the connections between chip RAM and the custom chips to consider.
EDIT: I'm pretty sure will be messed up on composite output too. But the games were both released before AGA was and that might be the reason they don't display properly.