Outside unit not running, inside unit is running, but blowin heat. Goodman unit MODEL CK-J60-1

In general the answer is yes. But no fan and no compressor points to a problem. Is the house heating using the auxiliary heat then?

https://www.repairclinic.com/Shop-For-Parts/a38b377d1442115/Model-CPLE301-Goodman-Heat-Pump-Parts

check your breaker or fuses at outside unit. verify you have 24 volts feeding outside unit replace outside unit contactor if you have the 24 volts and not starting.

is green wire from thermostat or from outdoor. retrace and change as needed. If not Goodman has a tech support number you can call while looking at unit.

Replace the capacitor on the outside unit.

This model of Goodman A/C the condenser coil get extremely dirty and what happens is when your condenser runs for a long period of time it pops the capacitor. This is the starting component for the compressor and the fan outside. the coil needs to be cleaned with a non acid condenser cleaner. Open up the side compartment of A/C look at the silver cylinder thats the capacitor if is looks swelled replace it.

The inside fan will run while the unit is in defrost. The electric heat strips should kick on to help prevent you from feeling this cold air. When the unit is in defrost it is essentially running in the A/C mode. You should make sure the electric heat elements are working then go from there.

sounds like you have a bad fan motor in outdoor unit or a bad run capacitor ck cap first you can go 1 size larger than listed on motor data plate

Replace the fan relay switch in the airhandler(inside unit).

If your running gas heat it's 5/8 3/8 tubing.If it's elec. heat it's 3/4 3/8 tubing. Etheirway 3/4 3/8 works for both. Use 6 wire for tstat from tstat to furnace or air handler, and you need is 2 wire from condensing unit [outside] to furnace or air handler or anything more than two.