My '05's blower motor keeps running when both the A/C fans are set to off and the engine is off as well. Left the car alone for 2 hours after it started happening and... it was still blowing! I had to unplug the 30 fuse just so the fans wouldn't kill my battery. Some say it's a relay, or the blower motor resistor, but it's so weird! However, I'm determined to fix it myself.

Any idea what it is? And how I could fix it?

 

A relay can absolutely cause that. We had one fail on the radiator fan on our Ford and I had to pull the fuse every time we stopped until I could grab a replacement (or it would kill the battery).

As with anything electrical, the right way to troubleshoot it is to get the diagram out and break out the multimeter. I usually advocate strongly against just throwing parts at things without proper diagnosis, but given a relay is only a few bucks, I'd probably toss one in first to see if it fixes it.