HI! Sorry, your experiencing problems in the game. I was low on time and couldn't properly bugtest the game. I'll try to get a good solution of your problem.
First, did the dialogue box disappear when you got through the dialogue? You have to press Z one last time to close it. You can't move if the dialogue box is still open. When it is closed, press arrow keys to move.
If it did disappear, then try pressing R. That will restart the stage. Maybe your soldiers bugged out and got too close. That happens. Just restart the stage and use the arrow keys to move. Hopefully it will work.
I'll test it myself too in case there is any problem with the game itself.
Let me know if the problem was solved or not!