Here's the GBC motherboard:

 

 

First, I verified that it still boots in this condition:



For comparison, here's a shot of my TI-84 next to the GBC innards. Looks like this just might work! It's going to take a bit of wiring to map the keys to the original TI-83 keyboard.

I will have the cartridge load in from the top.



Now, because I'm going to use the original keys on the TI-83, I need to find the pins on the GBC board that control the various keystrokes. After a bit of checking with a grounded wire, I managed to find 'em....



Above we see the pinout for the DPAD controls.



And for A/B/select/start. Again, these pins are "active low", and are grounded when pressed. 

So next, I take apart a broken TI-83 that I acquired. Here is the contact board for the TI-83 keys, all wired out to go to the GameBoy motherboard.



Here is it all hooked together. Somehow it worked! (Yes, that is scotch tape holding the telephone wire down.)



And here's the GBC board on top of what's left of the TI-83 innards:



And here comes the heavily modified back piece...



And here is it all done. You can kinda see Pokemon playing in this picture. (Yikes, looks like the clear button is upside down!)

Here's how the keys work out:
2nd = A
ALPHA = B
up/down/left/right = TI keypad
start = enter
select = +



Here's a better shot of it running. (The screen is so dim when you're so used the the Nintendo DS!)



And there's the game loaded into the back. You can see part of the bulge below where the batteries are. Not to worry, the back panel of the calculator stealthily slides over this!



So there you have it. It's a little clunky, but everything works!