Yesterday I lost power while I was running MAMP, and when it came back it could not connect. I've experienced this several times when I had to force quit the application and as a result have folders labeled notsooldmamp to access my old htdocs folders.

I just discovered a workaround however! If you launch MAMP, go to your preferences, uncheck the options to start/shutdown server on startup, things should be up and running again. This is apparantly a known issue that will be fixed in the next major release of MAMP.