Troubleshooting Is says something about a DirectX 9.0c compatible graphics addapter

Josh is correct!
From the Pets expansion on up the new expansion packs started using more shaders (makes all the pretty effects in the game) that your 6100 can not handle.
One expansion pack maybe it would play (just don't expect the prettiest gameplay) but all those others are really killing your graphics and having a weak cpu and low amount of ram like you're stuck with you just as well uninstall the game and play just the base game.

 

Thanks ...

Thanks,i need now to save money but lol nevermind...Thanks for the help very much~Oh and can you tell me wich CPU is best for playing games,i need to know what i buy next time crying

 

I would suggest you go with a Core 2 Duo . (something between 2.5 - 3 GHZ in speed)
Avoid the quad core and 6 core cpus that are out/or coming out because the game doesn't gain any advantage from the extra cores.

 

I'm also having this problem: "Failed to find any DirectX 9.0c compatible graphics adapters in this system! Please make sure you have a DirectX 9.0c compatible graphics adapter and have installed the latest drivers provided by the manufacturer. The application will now terminate."

It worked last night before I updated my video driver. I have a fairly new computer with DirectX 11 that should be able to handle this game.