I've had the Dawnguard questline become broken due to a "clearing a radiant quest location before you get the quest" issue in "A New Order": the bear that's supposed to be in the bear den is long dead (I believe I entered the cave and killed it before Dawnguard was even out), and now Gunmar is standing in the middle of the cave staring at a wall and warning me about a nonexistent bear.

Luckily, I've always been a PC gamer, and I'm wondering if there's any way to use the console to reset the dungeon or something.

Downloading/Installing the Unofficial Dawnguard Patch should take care of that issue for you. Along with several other glitches.

Guess I'll try that, then.

Maybe RecycleActor or Resurrect 1 (if you can find a dead bear to target)?

You can use the console command

resetinterior

There's a list of cellids http://content3.uesp.net/oblivion/cs/cslist.php?game=sr&rec=CELL