Is there any way to access the glove box if the door won't open?

You can't

I was able to get it open by using two flat metal strips in the top seam near each side and moving things around to try and get them where the latch mechanism were on the pin (There are horizontal pins in a grove approximately 1/4" away from the edge of either side of the glove box, and the handle is supposed to pull a hook back enough so you can release past the pin, but over time it gets stuck and then won't open). I liberally WD-40'd the latch mechanism and forced it back and forth for a few minutes, and now I can open and close it without any major trouble.

I had the same problem with my Cadillac Allante. Note: every glove box is different. The problem with mine was the plastic hinges and the rod that rotates to release the pins both rest in plastic "journals" and the journals had been broken because of someone kept forcing the glove box open. Since I could not locate a replacement glove box, I used J-B Weld to rebuild the journal clips and several other plastic parts behind the glove box cover and the door. It took patience, a little rusty model car building skills to repair the actuator rod and journals, but the repair was successful. I did use my Dremel Tool to shape the repairs. The vinyl covering was partially pulled away from the glove box door when I purchased the Allante, and I was able to remove the cover using a thin, narrow putty knife to break the adhesive used to hold the cover to the plastic door. To replace the cover was a simple process using light duty plastic spring clamps ( available at Harbor Freight) and Gorilla Glue. NOTE: the correct way to remove the vinyl cover is to pop the four round covers on the inside of the door and unscrew them to separate the cover from the door. The screw posts on mine were broken loose from the door. Used glove boxes are available on E-Bay form time to time. Black ones are few and far between. Red and Dk. Brown are more common than the other colors. All in all, my cost was