So I assume you're using standard legacy keyboard and no multimedia keys.
Unfortunately no answer concerning any other application which may steal focus or use global keys.
Maybe you can test if something has perhaps gone wrong with BS.Player's settings-file as follows:
(1) exit BS.Player
(2) rename the file "BSplayer.xml" to something different
(With respect to the location of this file, please read this post (click here))
(3) start BS.Player (which will then create a new settings file with all default settings) If keyboard keys now work, I'm afraid your initial settings have gone wrong somehow. BS.Player has now created a new one, but if you changed settings before, you'll have to do that again. If nothing has changed, you can if you wish (while BS.Player not running) re-enable your old settingsfile by deleting the newly created "BSplayer.xml"-file and renaming back the old file. 