Took the bottom panel off the dishwasher, saw the leak was coming from the water inlet valve. Ordered the replacement part at 6pm EST, paid a little extra for shipping (the $9.95 option) and the part arrived by 1pm the next day!
Using the how-to video on this site, I shut the water valve, cut the power, and then replaced the part without even moving the dishwasher. Took about 20 minutes and the leak is fixed! Very happy I was able to fix this problem myself so easily.