Yesterday after returning home I noticed the upstairs unit was not cooling. Checked the breakers and noticed they were not blown. Inspected outside compressor area and noticed no freezing on the coils and fan not blowing. Turned system off for about an hour and then restarted system. Outside fan motor would not start and system was making a humming noise and was warmer to the touch than the downstairs system that was running properly.

What are some possible causes for this problem?

You should not run the unit if it gets warm or makes funny noises. Call a repair person to properly diagnose your cooling system.