Well either the AP is broken, or the power adapter is broken. Depends, anyway something is broken and can not be fixed, I am sure of it.
You could get another DAP-1360 if you want to, you probably just got a bad version of the unit. It does happen. And since the v3.04 of the firmware was released, everything is stable and works fine.
Or you could go for netgear instead, not a big deal. However the DAP-1360 does have a lot of extra custom (or not standard) options on how you can runt the unit, once you set it up. Think it was six different modes.