I have a YORK HVAC unit, the blower works fine when I have the heat on, however, when I put the air conditioner on, the inside blower doesn't work. No air comes out of the vent? Is there a control some where which dictates the blower to go on and off based on heating or AC?

I would suspect and test at the thermostat.
Blower is usually the green wire, when set to heat or cool, red connects to green.

There are four wires Red, Yellow, Green and White. There are 5 slots to hook up these wires, namely W for White, Y for Yellow, W for White and two reds( R and Ro), the red is connected to Ro and all others are connected accordingly, White in W, Yellow in Y and Green in G. Should I connect the red with green as well? And leave both R and Ro empty?

Likely Red is from transformer, green is blower fan, white is heat, and yellow for cooling. Is this a new thermostat, any new wiring, or problem just developed?

I moved in this house in January, as it was cold outside, inspector did not check the air conditioner saying the oil in the compressor is all jammed due to cold, so won't be able to check it. However, when I checked in the hot weather, the blower fails to kick in. May be wiring was altered/changed/worked on, not sure about it though. Also there a two zones where the problem is, not sure if it helps in diagnosis. Thanks for your responses.

The fan relay is out on the control board.

For a test, you could disconnect wiring from thermostat, connect red, yellow and green. That should get blower and compressor going, if so, problem is in the thermostat.