If you press the green button and 'nothing' happens, open the Task Manager and check if GTASA.exe is running or not.
State which operating system you use. Always check if the single player version works.
On Vista do NOT install SA:MP or GTA:SA under the \program files\ folder. It will cause problems with access rights.
If Vista offers you to upgrade GTA:SA after closing, do not upgrade. If upgrades are set to automatic, set them to manual confirmation.