No power in r line after changed thermostat
check for 24 volts at the furnace. Some carrier boards will have a lit led even if the 24 volt circuit is non functioning. I don't recommend using a contact probe. I always recommend using a muti-meter. 
 Check from R to C. your looking for 24 volts. if no voltage, then check 3/5 amp fuse on board. If fuse is good, check voltage from transformer. 
 If you do have voltage From R to C. put a jumper from R to G and see if the fan comes on. if fan comes on, then you know the issue is at the thermostat somewhere.
 I hope this helps..