It appears "I re-stripped the cable end leaving the silver shield. Now, no signal" and "When I stripped off the shield and reconnected, I get one FM station" that the coaxial cable is providing most of the reception.
When the silver shield is connected, the coaxial cable functions as a conduit for the signal, and in general doe not pick up or receive any of the signal. When the silver shield is not connected, the coaxial cable can act as an antenna, although not necessarily a good antenna.
Something may have changed when you moved the coaxial cable, maybe an issue with the the connectors used to connect the long and short cables.
It will be a process of elimination.
Remember that it is all about the strength and quality of the signal where it is being received. Some may be able to receive a signal with the antenna inputs shorted, but that has no direct bearing on your situation and is not necessarily odd.
In terms of moving your antenna, changing the location of an antenna even a small amount may have a fairly large impact on reception quality. The first thing to do is to verify that there are no problems with you feed line (coaxial cable) and any and all connections.
Your current antenna location may be a good location in terms of reception and moving it may degrade your reception, or not depending on your particular situation. The point is you could move your antenna, repair any issues with the feed line and connections and end up with poorer reception. Make sure every thing is working correctly before experimenting with antenna location and orientation.