Recently, Parallels Desktop did not shut down correctly for me. When I went to start it back up, it just sat there with a spinning wheel, and a message saying "suspending."
I did finally resolve the issue. Here's how I did it.
1) Quit Parallels.
2) Open up the Activity Monitor. On a Mac, this is Utilities > Activity Monitor.
3) In the list of processes, look for one named "prl_vm_app". Select it.
4) Click the Quit Process button in the upper left. Choose to Force Quit at the prompt.
You should be able to start up Parallels Desktop again.