I have a Southwind IV ceiling fan with a light kit that is remote operated. It also has pull chains for manual controls. I have had trouble turning the unit on and off so I tinkered with many things such as the cords, the remote and receiver, even to changing the wall switch. I then disconnected the remote receiver and wired the fan to the outlet box directly connecting the blue and black wires to black and the white wire to the white. The fan works as it should, however the light fixture stays on and cannot be turned off with the pull chain. Have I done something wrong or can it be the pull switch that is not working?

Sounds like you bypassed the pullchain by mistake. Open the switch housing, it's an easy fix.