Update:
Installed the new battery today. Went down to the gas station to fill 'er up, and get the tires back up to the proper pressure. On the way there, I kept fiddling with the 4WD selector, and some strange things were happening. The PART TIME light started to flicker, and then shut off. I tried to switch back and forth between the different positions, and it wouldn't even light up anymore at all but I knew it was still in PART TIME due to how it was driving. So I filled up, and took care of the tires, and then on my way back to the house started fiddling with the lever again, and the PART TIME light came on again. Fiddled some more, and it popped into 4 FULL TIME! Then I left it there a bit, and tried to go into 2WD. CLUNK! It worked! I went back and forth between the different positions, and tried 4LO again, and everything seems to work now! Yay! I'm going to have to make sure this thing gets driven more than once a year now! Thanks for all the help everyone!