I just broke my headphone plug/jack. So it is now stuck inside my computer. How can I get it out?
If you can add a close-up photo of it, that would be excellent. Until then, I'll assume there is at least a millimeter sticking out. If so, try grabbing that with needle-nose pliers.
If that fails, you could CAREFULLY put a dot of Super Glue on the tip of a straightened paperclip. Press that against the headphone plug ONLY. Hold it very, very still for 10-20 seconds. If it dried correctly (fingers crossed!) you may be able to slowly draw out the end of the plug by pulling on the paperclip. (DON'T get it stuck to anything except the plug you're trying to remove!)
There's a very good chance that the socket is not completely enclosed (it will most likely be in the form of a springy piece of metal with a kink in it to lock the plug in place), so if you removed your case from your computer you'd be able to push it back the other way. It should go without saying that you should disconnect all electrical power before opening the case up and avoid touching any circuit board components.
I did something similar once by taking a standard cotton/Cue tip bud and cutting the stem about half way along, then inserted it into the jack and it fitted nicely over the top of the snapped of plug, it was just a case of pulling it out :-D