SOLVED

Replaced old resistor with the new one I had ordered to originally diagnose the problem and this stopped the noise. So, as it turns out, it appears that my original resistor went bad, thus frying the original blower motor. I replaced the blower motor with the new one MrMoPar sold me, running it through the original resistor. The fan now worked, but there was an awful squeal coming from the vents. I then replaced the resistor as well and the problem ceased.

Thanks for the suggestions and help from all.