I also thought I was at checkmate because I couldn't move my king in any direction, but the game said check. In that case, you can capture or block the direct movement of one of your opponents' pieces that is causing you to be in check... even if you can't see that immediately. If you can't move, the game displays checkmate and you are forced to start a new game.
Here's an example. My king, at e1, cannot move, because it is kept in check by the rook at g1 -- preventing movement to f1 -- and the queen at h2 -- preventing movement to e2 and f2. But I can block the direct movement of the rook by moving my knight from d2 to f1.
Indeed, the game says nothing when I try to move the king, but you have to know the game well enough to figure out why you can't make a certain move.