How do you know it won't transmit? Does it receive?
You may have a bad microphone PTT (push to talk) switch for example. If it's a used CB, the transmitter section could be shot from someone trying to transmit without an antenna, one that is short circuited, or has short circuited coax to it. To check your coax and antenna, you can use a Volt/Ohm meter to check for a short circuit, but it won't help determine if the length of the antenna is correct for proper standing wave ratio SWR messurments.