I had the same problem, and just played around and found this might be a simple solution. Take it for what it is worth.
I open iTunes, and I get the blank screen. Go back to the desktop. I control click iTunes in the dock. Play a song. I am running OS 10.10.4, and going to the notifications section click on the song that is playing. While in desktop mode, the menu bar at the top switched to the iTunes menu. Go to iTunes > Preferences (you may be able to bypass the entire control click process by using the short cut [Command-,] I did not try this). Once preferences opens, then the iTunes window will magically appear. If the box that says "Show Apple Music" is not checked, then check it. For some reason if that box is not checked, then it will not connect to the Cloud. That is why it gets caught in that loop and the magical pinwheel appears.
I have not retried it by unchecking the "Show Apple Music" box.
Good luck. I hope Apple fixes this bug soon.
Update. I shut down the computer, left it off for a bit. Started it, opened iTunes, and came on full screen no problem. You will have the "For You" menu on your iTunes wanting you to purchase the service. Just leave it alone, unless of course you want to purchase the service. DO NOT CLICK ON "GO TO MY MUSIC". It will automatically uncheck the box in preferences, and you will have to go through all of this again.
BTW, if this is the fix, and I just solved it for Apple, I think they should give me at least a year of free Apple Music Service. 😀
Unless of course, Apple did this on purpose in order to get people to feel obligated to purchase the Apple Music Service. In that case...ðŸ˜