if one works the other don't even with new battery its obiously faulty. 
 Or, only a guess,  if you have to set fobs to operate alarm when first installed  then try re-setting the offending fob.
like the radio when vehicle battery removed, you have to enter code to re-activate the radio. In case of alarm it may be by pointing fob at alarm and press buttons to activate/link to alarm
                
 bb
                
 February 2011