I was driving back from Boca Raton last night and I noticed that my DIC was dimmer than usual. Being an engineer, I knew a little tapping on the dash would fix everything. Unfortunately, it turned off completely! More tapping didn't fix the situation. I've only had this car a few months so I'm not yet familiar with all of the goings-on behind the dash. What could cause this problem? Should I just humble up and take it to the dealer?

If it is still under warranty, strongly recommend taking it to the dealer. Being an engineer you should know the goal sometimes is to fix the problem using the most efficient process.
If it isn't and you call them and they say "We will have to charge you", then I assume it is a DIY task.
Personally, I am not sure how to fix this. I assume it is a loose connection since you hit it and it stopped.

BTW: Welcome to the board!!!

You're going to find LOTS of information and helpful folks on here.

Shine a bright flashlight into it while the car is running. Do you see the words/numbers?
If you're familiar with backlit LCDs,... the LCD functions separate from the backlight, so you could figure out if it is the whole thing or just the backlight thats out.
and as a note, my old grand prix has a small portion of the backlight go dim, so I don't know of the backlight functions as a whole or is separate pieces.

If the whole thing is dead, could be the connection in the cable behind the unit. (hopefully?)

Here's a link to replace the bulbs in the DIC.
The link is not up at this time, but keep checking it. It goes up and down quite often.
http://www.claver.com/grandprix/howtofix.htm

It's a fairly easy fix if your bulb's are burnt out.
Basically remove the dash trim ring and you'll see how the DIC is mounted. Remove the DIC and take off the back cover on the DIC and there are your bulbs.

Thanks for the help guys. I never could get that page to work but I did a little surgery and managed to pull the DIC out and get to the bulbs. All three were burnt out. The cool thing to do would be to replace these old light bulbs with some white LEDs so I never have this problem again. But, that will have to wait until I can get back home. I'll try to get some more bulbs tomorrow.

I forgot to mention, be prepared to be raped by the dealership. I think I paid $11 for 2.