Ford Repair: 1994 thunderbird starting problem mystery, starter solenoid, mechanic friend

Question
Hi Tony,
I have a problem here that has perplexed my mechanic friends and my ford mechanic friend. When it is cold out(below 25 degrees), when I turn the key to start the car, it doesnt do anything. but if I hold the key in the start position from anywhere frm15 seconds to 1 minute , then the car turns over and starts. Also, after the car has run for a minute or two, and I shut it off, I can turn the key and it starts right away, and obviously anytime after that as long as the engine/car is warm. It started last winter, and they told me to replace or check the trigger wire, but all seems fine there. Its just when its cold out. also, about that time I started getting a battery drain overnight or when the car sits for extended hours, it can drain the battery in 40 hours where it wont start because the battery is dead or almost. are these problems related , or two seperate ones. The car now has 130,000 miles on it. it has a 4.6 v-8, with every option ford had for the car back then. Otherwise the car runs strong, and good, and doesnt use oil at all.
  any idea on this one???
 I am Very mechanically inclined by the way

  Thanks in advance for answering , and volunteering your time on here
   scott

Answer
Hello Scott, Check the starter solenoid wire, it is a single wire that connects to aspade end on the starter solenoid. They will corrode and not make a good contact, colder weather and any hunidity can effect it. You may also check the relays for the pcm ect. Hope this helps Thanks Tony