I decided to give I²C a last final effort, which included tons of searching on the internet. The problem is that other than the start and stop bits, the interrupts are never triggered. I double-checked so many things and actually found a few things to fix, although it didn't really make any difference with the results.

So after reading about SPI since last night, I was able to figure out the code for the Arduino and get that programmed pretty easily as a master and set it up to send out data every half second. I did some reading about the PIC and got that set up so it initialized and would display some data on the LCD if it received any data. On the first attempt, I was able to start displaying information on the screen. It looks like I'm going to use SPI despite the additional wires/pins it uses because it works. After doing some more reading and fine tuning, the next step will be to get specific data flowing between the 2 and then I'll program the PIC to start reading and storing values from the PWM (remote control) receiver and storing it so that the arduino can just query the PIC chip any time it needs those values. After that, it'll be time to get to the fun part and actually creating the main program that will run my robot.