Since upgrading to TorBrowser 3.6.3, I have noticed that after the first session when I tried to restart TorBrowser, Tor would show that connection was made but no browser window would come up! Both tor.exe and firefox.exe *32 processes show in task manager though.
One option is to go back to 3.6.2 as the Tor version hasn't changed as suggested by some users on the announcement blog post (see comments). However, as 3.6.3 contains several security fixes for Firefox, I wouldn't suggest downgrading.
The second option: delete the lock files in "Tor Browser/Data/Tor" and "Tor Browser/Data/Browser/profile.default/". After this the TorBrowser brings up the browser window as it should.