Pursuant to your cold radiator problem. It could be due to two possible causes (as far as I can tell).
1. could the radiator be blocked with some form or gunge/junk. Has the water level in the header tank been allowed to fall recently (maybe bringing all the residue from the bottom of the tank with it). The only way to confirm this is to remove it and flush it.
2. the radiators could be set up incorrectly. Has there be any modification to the plumbing lately ?. Is the radiator that is giving the problem a new one recently fitted ?. The hydraulics of you hot water system is that the water will want to circulate through your system TAKING THE PATH OF LEAST RESISTANCE. Each radiator should have an on/off valve on the supply (or upstream) side plus another **similar valve on the return (or downstream) side. ** It is an on/off type valve that is adjusted by the plumber when the system is set up. It is left PARTIALLY OPEN and the handle is then removed so that it cannot be tampered with. The degree it is left open will affect the amount of water that is left through the radiator. For example, the radiator nearest to the pump will have this valve closed more that the others THUS FORCING WATER TO FLOW TO THE NEXT RADIATOR, AND SO ON. Once set up all the radiators should receive the same amount of hot water.
To confirm if this is your problem I suggest you close all the normal on/off valves on the other radiators. The water will have no where to go except the cold radiator. If the radiator then heats up then you know there is no problem with the radiator, per se, just a hydraulic problem. You would then have to 're-balance ' the system by adjusting the aforementioned **valves (suggest you get someone with some experience to do this).