Did you try the remote for the other fan?
If the remotes are the same type you may have mixed them up. I'm asking this because you said the first remote worked the other fan. This would mean both fans have the same dip switch settings. As joe suggests check for power to the fan. I've seen a loose wire nut cause this problem before. Also if the fan has a light kit and it is working then you know you have power to the fan. Then the trouble could be a bad connection from the remote output to the black fan wire going to the fan. I might also suggest trying the fan pull chain speed control and checking the reversing switch sometimes the switch isn't set all the way. If this doesn't work disconnect the remote from power (shut the power to the fan off first) then rewire the fan directly to the circuit turn the power back on. If it works then you know you have a good fan and i bad remote. Thats about all I can think of. I hope you find the problem. Let me know.