If the green is not hooked or broke at the t-stat it only messes the fan up in the ac mode. The fan is controlled by the furnace in the heat mode.

So its either a bad relay or the wire is broke right

Yea, did you check you green connection at the t-stat?

Yes it is connected

OK one other thing you can try is to take the t-sta off and jump between r and g and see if it comes on. If it still does not then it is most likely a bad relay and you will most likely need a new fan control board.

OK thanks for your help I appreciate it

No problem. Also. To get cooling for now. You may be able to switch the cool wire on the control board to eac which is a different relay.

The control board should be in the bottom door of your furnace. And the cooling wire should be black and hooked where it says cool on the control. Turn the power off and move it to eac and see if that works. It will not work for ever that way but will keep you cool till you get a new control