I noticed CS wont runs on the newest Amigamerlin too. The cure is MesaFX. This "advanced" little masterpiece of dborca will let you run CS properly.
I will take it step by step:
first you need to
download MesaFX itself. Just take the newest if you dont know what to take.
Then you will need to extract all the files to a new folder. I would advise to only use the
opengl32.dll file. The rest you can throw away again.
After you extracted opengl32.dll you will need to move it to the CS folder. Assuming you are using Steam the default for this is :
D:\Games\Steam\SteamApps\username@provider.com\counter-strike\
Now you will notice that the mouse dissapears in the Steam menu when you load the game. To solve this problem open the console with (~) and type : vgui_emulatemouse 1
Then play CS all the way

As for Quake3, it should work just fine. Try putting the opengl32 file in your Quake folder maybe it helps.