When you removed the red stat wire from inside the furnace, you reported back that the blower did not come on.
When you disconnected the green wire from the stat, you reported that the blower did come on and stayed on.
You have not performed a continuity test on the red & green wires to determine if the wires are shorted together.
I think you'll find that you do have continuity between the red and green stat wires.
Disconnect the red & green stat wires from inside the furnace and from the stat and perform a continuity test with a meter.
Otherwise, hook the stat up to the furnace using a few feet of new stat wire and you'll find that your problem goes away. In which case all you need to do is replace your existing stat wires.