[Tomboeg]

I assume this also happens in Single-Player.

It looks like there is some issue with your keyboard.
Like Vince said, it seems like your keyboard doesn't register you holding the key and rather repeats the 'w' command walking key.

I see that you haven't reinstalled gta-sa yet.
Perhaps this might work. It is possible that some of your files have been damaged or corrupted.
This is the first time i see this.