You must have a very old hard drive, as SATA hdd's do not have a place for pins to go into them. Besides trying a pair of small tweezers (perhaps the likes as to which someone who repairs jewelry with), I can't think of a way to get the pin out. Perhaps the use of a magnet? Maybe even taking a straight pin, put a very small amount of super glue onto the tip, letting it nearly dry (to make it more tacky), then using it to touch the broken pin to pull it out. These are just ideas that I myself just came up with, so I don't know if they'll actually work. I did a search online, but I can't seem to find anything in forums about how to do this.
Nonetheless, if any of these ideas or an idea you get elsewhere works, let me know about it. I'd like to know a tried and proven way of doing this, myself. And should I come across something, I'll be sure to update. Thanks and good luck!