So I took my new AR build to the range for the first time to get it zeroed in. It was supposed to be a great day of shooting with my brother who was in town from Ft. Bragg, but it didn't turn out that way. The front sight post got stuck and would go down, but not up. My brother was confident he could fix the issue by applying a little pressure and sure enough he snapped the top section of the front sight post off, leaving the threaded portion stuck in the hole. Now I have no way of backing the threaded part out (picture a screw without the head). I was able to remove the spring and detent. Any suggestions short of buying a new front sight base?

Is there enough room to get a pair of hemostats down to grab the threaded section?

If not, another option would be a touch of JBWeld on the part that is broken off, insert it into the FSB, and try to remove the sight once it is cured.  I'm guessing it will spin right out without the detent in place.

Also you can use an easy-out, they can be found at any hardware store and are made for removing bolts with broken heads.

I take it from your description that the flange and the sight post is what broke leaving the threaded portion in the front sight base.  There is a chance you could try to drill it out but that is tricky.  Maybe you could drill a small hole into the top of the screw and then tap an extractor into it to back the screw out.  Some people have success using heat/cold to loosen things up.  I have heard people have used cans of dusting spray (canned air from office depot).  You can turn the can upside down and the propellant comes out very cold to freeze the bolt.  Then it may shrink enough for the extractor to break it loose.