The Nexus 6 hasn't been out on the market for very long, but apparently the AT&T version has run into some issues… at least some of them have. Apparently at least a few devices had issues with bad software (the phone is one of the first to run Android 5.0 Lollipop), displaying a blank screen when turned on. As you can imagine, that makes the phone hard to use.
Newer model: Nexus 6P
AT&T's ordered stores to ship their Nexus 6 stock back, with replacements already en route with corrected software. Said Motorola in a statement on the issue:
We delivered a small number of Nexus 6 smartphones with incorrect software to AT&T customers who pre-ordered. The incorrect software prevents the phone from starting up properly. We will provide replacements for consumers whose phones are affected. The problem has been corrected and the phones currently shipping are fine.
So have no fear. As always, if you're having an unresolvable issue with a new phone, you can get it replaced at the store as Motorola advises.