I have a 2002 F20 Super duty 7.3L with just 125K. I have been having trouble starting the engine when the temps are around 40 degrees. Batteries are both about 6 months old. I live in Louisiana where winters rarely stay below freezing for any time

When i turn the key to start, nothing at all happens and all the lights on the console go off. Starter doesn't even begin to turn over. If you wait about 10 minutes and try again, and turn the key really hard, it will usually start.

I was thinking this was an ignition key issue, but it doesn't seem to affect starting when the temps are above 50. I have checked the battery connections and they are tight.

Has anyone else seen this kind of problem?