DIAGNOSIS The drum unit and toner cartridge are separate parts in this printer, and the drum has a finite life. That message is telling you the imaging drum unit itself has reached its end, regardless of toner status.
FIX You need to replace the DR310 drum unit. Open the front cover, pull out the toner cartridge first, then you can slide the black drum unit out. Pop the new one in, reinsert the toner, close the door, and the message should clear. The printer will reset the drum counter automatically.
IF THAT DIDN'T WORK If the message persists after installing a genuine Brother DR310, there might be a dirty connection. Power the printer off, remove both the drum and toner, and use a dry cloth to clean the gold-colored contacts inside the printer where the drum slides in. Reinstall and power on.
HEADS UP Yeah, this one's common and catches people off guard. The drum lasts for about 12,000 pages, so it's not something you replace often, but you definitely need to buy the separate drum unit—a new toner cartridge won't fix it.