I recently re installed Football manager 2010 after a long time not playing it.
But when i enter the serial number on steam it says that the product code you have entered has already been activated by an existing steam account and is therefore invalid.
How do i fix it?
You only need to enter the serial number once and that is the first time you install FM, once that is done the serial number is connected to your steam account. Have you created another steam account since you're entering the serial number again?
Open steam go to Library, click on Football Manager 2010, click install (in the middle near the top). It will install from there, and I don't think you'll need the number agian unless you're installing on another account.