I have a 10-12 year Electric Goodman ac/heat unit. Just recently The fan runs constantly. Even in off position. I have replaced the thermostat. I have swithched the thermostat from auto to on several times. I have switched the power source box to off and on several times. Is there something else I can try before calling the repair man? And what could be wrong? I still have heat and cool air.

It could very well be a stuck relay.

Can I unstick it?

Usually no. You can try tapping on it but I wouldn't hold my breath and even if it did become un-stuck it will no doubt stick again.