This thread finally helped! Thanks for those that posted tips you'll see which I used below.
I just got a new Apple TV and everything worked fine, even Airplay from Mac/iPhone/etc. to the Apple TV (ATV wired, Mac wired, iOS devices on wifi same router/DNS server), BUT, the Apple TV could not find my iTunes library...I searched and tried all kinds of things, turned off home sharing and turned it on a number of times, restarted everything, nothing worked. Being new, and freshly updated, I didn't see the need for a restore (as you can see below, it didn't need it).
I did several things at once, so, not sure if it was one or the combination (MBP mid 2010, OS X Yo, iTunes 12 ...ATV3):
1) Changed computer name on Mac (System preferences>Sharing) (hint: even if you don't use sharing, do this, when you share your iTunes library, you are using sharing, but it doesn't show here). (I hadn't done this, it was still MacBook Pro 😊).
2) Changed Library Name in iTunes (iTunes>Preferences>General) (Turned off Home Sharing first)
3) Reset PRAM. ...Put ATV to sleep, then unplugged, turned off router, restarted Mac holding down command & Option & P & R keys, waiting for chime twice, let go.
I then turned on the router, waited a min., plugged in ATV, opened iTunes on Mac, etc.... now works like a charm 😀
If you tried 1 and/or 2, but, not 3, I highly recommend 3, it can solve some issues because some preferences on the Mac get reset.
BTW, the issue was with the Mac...I didn't bother turning off home sharing or doing anything special with the ATV, other than cutting the power, plug in after restarting mac and router.
Note: I set up my Apple TV automatically w/my iPhone (BT on), just put it close to ATV and it'll come up asking for iTunes password...easy breezy, I recommend this. (None of ATV settings were the problem.)