Ford F-150 will not start and gear shift can not be moved when key is in ignition. Lights on dash very dim and slowly go out.

Check your battery. On my 2003 I could not shift out of park. Calling the dealership, they told me if the battery is low enough the vehicle's shifter cannot be moved. I used a jumper cable and it allowed the vehicle to be removed from park. Sounds like a battery problem since the dash lights dim and dim out.

Turn the key one click,then put into neutral,then start

When key is in ignition-key can not turn at all- this prevents from moving the gear shift out of park.

This is an update on my 2014 Ford F-150. After a whole year of investigating why it wouldn't start, it ended up to be the "Body Control Module." Which is the fuse panel behind the passenger kick panel. It had a short in it and when I slammed the module with my fist it came alive and started. Who would ever know. Wonders never cease.