Broken glove box hinges are another common issue with the B6 A4 and S4 (maybe the B7 A4/S4 and RS4 too?), if yours is broken, it’s broken, there’s not much you can do about it. You either replace the whole thing or mess around with brackets from your local hardware store and try to come up with something that looks respectable. I’ve seen varying degrees of success with this over on audi-sport.net, but by far the best way to deal with it is to stop it happening in the first place.
Here’s the glovebox out of the car showing the hinge/damper mechanism..
And here’s the cause of all these broken hinges!
You’ll notice this isn’t the hinge, this is the soft-open damper mechanism and light switch. Over time this thing stiffens up and puts loads of extra stress on the hinge, eventually snapping it or opening so slowly that people force it open and snap it themselves.
You need to remove it, take it apart and lube it up.
To get it off the glovebox the little split pin needs to be pulled out (needle nose pliers will do the trick), this will release the arm that attaches to the glovebox door and allow the whole thing to rotate. You twist it maybe 45 degrees or so until it comes free from the glovebox.
Seeing it all in bits should give you an idea of how to take it apart, but you just have to carefully pry the end off (that houses the light switch), and then pull out the arm with the rubber end.
Coat the barrel in something slippery. “SwissJetPilot” from thettforum.co.uk recommends, “Silicone and mineral-oil-based lubricants are the best choice since they won’t attack most plastics.” (thank you for your comment).
Then slide the arm back in (obviously rubber end first).
Reassemble and you should find there’s much less friction and less stress on the glovebox hinge. A really easy little preventative fix.