One Cold Radiator

I have one cold radiator in my house and i am certain it is the last one on the flow side. The two 10 mm pipes either side are also cold to this radiator and the pipe from the rad before on the return side of that rad is only luke warm if that.
I have drained the system and added sludge remover to it and that has been in the system for 24 hrs and still the same.
I am unable to bleed the offending rad as the bleed screw has sheared off!But am i right in saying that the flow pipe to this rad should be getting warm anyway?
any ideas would be appreciated.
p.s it is an open system
pps i also think this is a single pipe system

Not a lot of point doing much more until you determine if it has air in it. Is the bleed screw in a hole directly in the rad or is it housed in what looks like a nut ? If the latter, you can bleed it by slackening the nut and replacements for these are in most diy sheds. If you have the former, I would remove the rad and check for flow at the valves (and fit a new rad so that it can be bled).

Thanks for your reply bathjobby. The bleed screw that has sheered off is threaded directly into the rad so i am unable to do what you suggested. I will, as you have said, take the rad off and check for water at the valves, but, there is another problem about doing it this way. The valve is a TRV which is stuck. I have removed the head and sprayed the pin with wd40 but it seems to have given up the ghost as it does not pop up when pushed down. So i will have to replace that valve with a lockshield and take it from there.
Anymore ideas would be appreciated