When I say 'stuck' I am referring generically to any number of relays or switching devices in the furnace relative to that circuit... we will get into more detail later, if needed, as we progress with the trouble shooting.
If the largest tube attached to the outside unit, the one that is insulated and a bit larger than the size of a mans thumb, then the compressor inside that unit is not operating... the tube runs hot in heating mode and cold in cooling mode.
If the air filter in the furnace is dirty, the heat pump coil attached to the furnace will over heat and trip the high pressure safety cut out mounted in the outside unit.
Make sure the air filter is clean and none of the air vents are closed off.
You do not need to do the wire removal tests if the tube is not hot.
I also need to know how old the system is, and if you have furry pets in the home, that can clog the heat pumps A coil, above the furnace in a few years.