So the key was used to lock it and will not unlock it?

First thought is to see if the bottom hinge screws are exposed or not. If they are, you should be able to remove them and tip the box out from the bottom. If lucky you may then be able to reach the screws that hold the latch anchor at the top and remove them and get the glove box out.

If the hinge closes over the screws and covers them there is very little you are going to be able to do. That is also going to apply if when attempting to pull the bottom of the glove box out you cannot get enough clearance to reach the anchor screws. In either of these cases, glove box damage is extremely likely, and may not be preventable. In that case, the first step is get a replacement glove box! That way you know you will put it back together and keep the car nice. Just never plan to lock it again if possible.

With the replacement glove box in hand, examine it to create a removal of the original plan. One method would be to cut around the the entire lock assembly. A dremel tool will do fine, or else drill intersecting holes. Now you can remove the glove box, and only have the lock and anchor to deal with. If you have the anchor that goes with the "new" one, which I'll assume will probably come from a used car, then simply unscrew the anchor, and install the new box. BTW, this method will probably be the fastest. If you dont have a new anchor. You will need to cut the latch out of the existing one. If possible, remove it to put it in a vise on a workbench and it will be alot easier.

Have you tried inserting the ignition key and turning the lock back and forth from lock to unlock positions several times. (Make sure you are using the full access key and not the valet key.) If the lock cylinder can be rotated, try gently squeeziing the two oposed buttons while turning the lock cylinder back and forth, as in picking a lock. Can you feel anything happening with the stuck button?

If you can not turn the lock cylinder with the key, it may be that one of the tumbler pins is stuck in the far up position possible with small piece of dirt jammed under the pin. Try putting in a bit of lock lubricant and work the key in and out several times, and wiggle it around.

Thanks guys. I'll try Jemdandy's suggestion first, since it's the easiest. I'll let you know!

I finally had the time to take the car to a local lock and key company. The technician simply popped the plastic cover off of the lock itself. Then, he popped out the pin within the lock. It was the shaft inside the mechanism that was broken. He simply replaced the part, reversed the process and snapped the cover back on. Total cost: $30.00. My only regret? That I didn't do it sooner.