iTunes shows as running in dock but cant open or quit, force quit, or even shutdown computer. Running OS X 10.10.3, don't know what iTunes as can't open it!
I would suggest to use the Force Quit method on a stuck process.
Hold alt+cmd+esc then select the iTunes from the list to force quit.
Now restart iTunes and see if it behaves.
Following the above use Terminal to see which processes died in the past 7 days.
ps aux | grep -w Z