Just to clarify, normally both ends of a radiator have right-angled valves that connect rad to the house pipework. One has a splined plastic cover over it and is used to turn the rad on/off. The other end often has a smooth plastic cover over and isn't intended to be moved once set up. Prise the cover off and underneath is a brass shaft (it is actually the same as the other side but with a different plastic cover). This valve is used to set-up the flow of water around the system - called balancing. If a CH system is not balanced, the water merely rushes to the rad that is closest to the pump/boiler, goes round it and back again to the boiler to be reheated. The rads that are furthest from the pump/boiler don't get a look in, and remain cool.
By balancing, the rads closest to the pump/boiler have the valve that I am referring to permanently restricted by turning the brass shaft down (clockwise) - this restricts the flow through this rad and forces more of the hot water to the rads further distances away. It takes a time to balance and normally, once set up, a householder has no reason to go poking about trying to rebalance.
All I am suggesting is that if the lockshield valve I am referring to has been turned down (clockwise) too far, this towel rail rad is not getting its fair share of circulating water.
The technique I described in the first email is how to adjust.
If you are saying the lockshield has been fully opened so that both valves are completely open and you still aren't getting any hot water through, then something is likely to be in the pipe blocking it - sludge perhaps.