I had a similar issue with an HP switch (2910-24G-PoE+ al) and 7982's. I would get the orange blinking PoE light on an HP switch, tested with W_15_08_0012 and W_15_12_0011. With the firmware downgraded to W_14_38, the AP's powered up, but I didn't want to revert the firmware. Also, tested on a CIsco PoE switch, the AP's would not power.
I RMA'ed one of the 7982's and it worked on both the Cisco and updated HP. The rest of the AP's (being used with Ruckus PoE injectors) are currently being RMA'ed. The existing "broken" AP's had serial numbers starting with 3213 and 3313, while the new AP started with a 36. This lends credence to another forum posting about a change in hardware for the later revisions of the 7982's. If you are having a similar issue, please try RMA'ing at least one AP to test, even though you may not think it will fix the issue.