When you say "start up Parallels", do you mean that Parallels itself fails to fully open when just launching the Parallels app from the Mac Task Bar? Or do you mean that, after successfully launching the Parallels app, the Windows VM hangs when you try to open it?
* If the Parallels app itself won't open, it sounds like you might have to reinstall Parallels.
* If the Parallels app does open but the VM hangs, try rolling back to a previous VM state. Alternately, you might have to ditch the VM, create a fresh one, and reinstall Windows.
Whatever the case, any more detail you could give us would help.