I sat in the car last night for 10 minutes after I shut the engine off and the fans never shut off, so I ended up pulling the fuses. After the car sat overnight I went out and put the fuses back in this morning and both fans fired right up. So for some reason they are getting a constant power signal to run, even when the key isn't in the ignition. So I went from the old fans that wouldn't engage at all (which caused the overheating), to new fans that won't shut off! I tried everything I could think of, but in the end I took the Edge to a mechanic this morning. My only hypothesis is that the coolant temp sensor is broken, causing the PCM to think the engine is constantly overheating and causing the fans to run. Thanks for your help. I will post whatever the mechanic finds..