ITunes 12.3 issues have self-corrected
I upgraded to El Capitan and ITunes 12.3 10 days ago only to discover that ITunes no longer responded. It would open but none of the menus or controls would function. It also froze my IMac requiring me to power down manually. Today I was talking to an Apple Support rep about this issue and using their screen sharing app when ITunes suddenly became fully functional again. Go figure! I think the issue has to do with the app downloading the music library. My library has several thousand tunes and it may take some time to fully download the first time you open ITunes 12.3. Try leaving the app open for some time and see if that helps.
iMac, OS X El Capitan (10.11), Early 2008 IMac