Damn, I was afraid ripping the original board out might not have been a good idea. I don't think it's been damaged, but it won't be able to be powered by the Jeep's original batteries anymore, and it can't even reattach itself to the battery compartment because I filed that down to be nice and flat for the Uno. Anyway, here are the most high-res pictures I could get of the board, front and back. Two questions:
1) If I use the original board from the Jeep to control the motors, do I not need a Motor Shield anymore?
2) Will I still be able to power the original board with another type of battery?
And I don't know what an IC is, but on the back of the board it says 'RX-2022B(SMD)'.
Yep - that's a standard RX2 half of the TX2/RX2 chipset; it's a very common R/C chipset, and fairly easy to interface to. This is the huge thread on that chipset I had a hand in:
You might still be able to use the board, but you need to first figure out what battery it used, and try to get it hooked up like it originally was if you can; the main reason being that some of these vehicles use 5 volt logic, while others use 3 volt logic (if you use the wrong levels with the wrong board, it either won't work, or you'll burn the board out).
At this point, it would probably be better to just use your multimeter to find out what the stall currents of the motors are, then buy a couple of motor driver boards or shields to handle the loads, and go that route.