Do you want F-keys work by default?
When did they work last time, on what OS? Windows?
There is a Logitech tool (windows only) for keyboards/mauses but it useless if keyboard doesn't have internal memory...
Try maybe piper
(in the Software Center) and solaar
(in the Software Center)
Other option is remapping tool, but I don't know which one...
BTW I have Logitech wireless keyboard, F-keys work via Fn key, I hate that.