I actually took my car to have it fixed. The connector (harness) was indeed the problem with the blower only working on high. The AC needed a new clutch.

So was the harness the problem? I am having the issue with the switch problem - it only works on high. (And now, to add to the aggravation, my AC has gone out.) Anyway, we have replaced the switch, resistor, and relay and nothing helped. I'd like to talk with you on this if possible. Thank you!