My goodman air unit wont turn on but has power to the relay and can be manually overridden at the relay but doesnt sound like the air handler comes on. I changed the batteries in the thermostat and even switched the thermostat with my second unit on opposite end of house. I also thought it might be the run capacitor again so I changed that already. Any ideas?

Check the transformer. There could be a chance that the transformer is out. If you mean you can manually turn on the unit by pushing in the contactor switch in then theres your problem The thermostat engages the low voltage side of the transformer sending 24 volts to the contactor switch engaging the system if this transformer is out it will not engage the contactor to turn on the system.. Also on the air handler at the door on the bottom of the airhandler there should be a small circle of clear plastic by looking inside of this circle you should see a green led . If you see a red led it will be flashing count the flashes as they are emmited and once you see the pattern they have then remove the bottom door of the airhandler and on the bnack of this door is a code that corresponds with the flashes i.e. 3 red flashes, pause, three red flashes. The code will tell you what is occuring within the system. However, If your system is not a newer model it may not have the leds as I have described. If that is the case the first part of this solution may correct the problem.

Good Luck on your repair

Dave