Is the yeast dead?

I'm brewing an IPA. It has been in the primary fermenter since July 4th. I'm about ready to keg it, but I've never fermented a beer this long before. My question is, is the yeast still alive to utilize the priming sugar for carbonation, or do I have to force carbonate this batch?

There is still plenty of yeast in suspension to carbonate naturally... it just may take a couple more weeks.

Nope. There is still plenty of yeast in there to carbonate the beer. And the beer may very well be the best you've ever made.

^agreed. They are "sleeping". Give them some fermentables and they'll wake right up.

If you have been conditioning an ale it at room temps, you should still have enough live yeast in the beer to just be able to add priming sugar for carbonation. There are some ale yeasts, like S-04 for example, that flocculate extremely well and pack into a tight cake, so that when you package it sometimes it doesn't carbonate as quickly, but in my experience it still gets there.

In some cases where you are lagering at lower temps for an extended time, a lot of the yeast will drop out which can cause problems priming. HOWEVER even in that case, you can still add a bit of yeast to your priming solution at packaging time, and that will help things out.