562T remote starter

Now I've done a lot of research, but I'm stuck. 

I'm installing the DEI 562T in a 2002 Explorer and I've got everything hooked up as required. I've even installed an 1100F bypass.

The trouble is, I can only get it to remote start when the key is in the RUN position.  It will not start with the key just inserted in the off position, which leads me to believe that the 1100F is not the issue.  Also possibly related is the fact that I cannot seem to program the 1100F with the 2 factory keys per the instructions (but again, this does not explain why it will not start with the key in the ignition).  The 1100F is wired right, and even allows me to program it for "ground when running" mode, but will not accept the programming cycle with the keys.

I'm pretty new at this and stumped.  Please, I am desperate for help!

Thanks!

Twelvoltz:  Thanks for the quick reply!

Yes, I've attached the pink wire from the 562T's satillite relay to the RED / lt. green as instructed.  I just probed it while attempting to remote start the car with the key in the ignition OFF position and got no voltage.  When the key is in the ON position I get 12V constant.

I think it may be something with the starter relay?  When I remote start (with no key or with the key in the OFF position), the gauge cluster lights up, I hear the door-open chime, and hear the starter relay click.  It does this three times (the default starting attempts by the 562T?) and then goes dormant again.  But if the key is in the ON position, it starts on the first attempt.

Again, thanks for the quick reply!!