Is it just F1 that's not working, and all the other F keys work?
There's a feature on my keyboard (a wireless Micro$oft one) that has "alternative features" for all the F keys, for example "undo", "open", "reply" (none of which work), but these require "F Lock" to be switched off, disabling the function keys' usual actions.
Example: PrtScn and Insert share the same key. But Insert is on the front of the key, while PrtScn is on the top. This means that when F Lock is on, the key acts as an Insert key, but when off, it acts as PrtScn (meaning that I often forget to turn "F Lock" back on after taking a screenshot, and then wonder why F1 doesn't work for showing scores)
So, check your keyboard for anything like this.
Just a thought.