Did the stud break off from the head or did it just unscrew itself?

In your first article you said
So I started tightening it. Well it just kept turning and turning an then I noticed that the Bolt was actually coming off the head
My question is if you were tightening it how the hell was it worming its way out? Even if it did bust I dont see how tightening it would make it come out. Are you sure you were turning it the right way?

If it just unscrewed a little loc-tite and a new stud would be all you need. It might also be a good idea to get a thread tap of the right size (size of the bolt) and clean any debris out of the hole.

If it broke off then you would need a bit extractor that you can buy at places like Ace Hardware (good store for parts by the way) and what ES said a helicoil kit. Still though you stated at in your post that it was coming loose when you tightened it so you probably dont need a bit extractor. Care to better explain just what is wrong with the stud? Youve got me all sorts of confused.