I had a problem today I solved in the following way:
I checked the log file at "home/.config/PyBitmessage/debug.log and ~debug.log.1" to troubleshoot the problem.
This is the Linux path so on Windows you may have to look somewhere else, but that is what to look for.
My particular problem was due to an incorrect system time, but checking this may help you solve other problems as well.
Unresponsive/message not sent/received: It seems BitMessage often gets "stuck". Under the sent tab you can see if your messages have actually been sent.
If your messages are not sent after 10-20 seconds rebooting BitMessage may help. You may have to do this several times.
(We know it is crap and will work on replacing it)