With GPS on, it reacts to GPS-Data. You have no position fix yet, there is nothing to see in Lat/Lon. Try to switch GPS off. The LED on the button turns to red. Compass is switching to orientation sensors and gyros.
Your orientation sensors are not working or the sensors are not calibrated (the "INFO" on the upper left button is in red colour, should be white colour, when well calibrated). Move the phone around all axes to calibrate the sensors. "INFO" should change from colour red, via orange and yellow to white). Then, if sensors working you should see a reaction by turning the phone around x-axis. Lay it flat on a table (the blue arrow indicates this), give it a turn. Make sure the compass is in "HIKING-MODE", not in "CAR-MODE". To prove that, do a longlick on the mode-button to get into the configuration-settings. Display "turns" to the opposite, then. There are the hidden configurations. When done, click back to go back to the compass-view.
If it does not react to anything, there is something wrong with your phone. If you own another one, try it there to get a feeling what should happen and what not. Read the documentation please.
Maybe this is the reason, for your problems in downloading compass related stuff from Google. If your phone reports limited capabilities (independing from what it should by the manufacturer) then Google prevents downloading it, because it will not work.
Is it a refurbished phone? Maybe the sensors really don't do what they should. I have a program for testing the sensors. Unfortunally it is to large for upload here.
play.google.com
not found on this server ? so I chased it down a bit:
