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This indicates poor circulation unfortunately. So either it's blocked or the pump is set to low or the system may benefit from balancing. So make sure the radiators are capable of getting hot by turning off all the others. If they get hot you will need to open them all back up fully and use the balancing valve to adjust each radiator down until you get an even heat across the whole system.
Yes old rads could be sludged up. If you remember water will take the path of least resistance. So if you have dirt and 10 mm pipe it will not flow to that area when it can divert down 15 or 22mm pipe.
Turn all other rads off to see if you can get them hot then it will be clearer as to what needs doing
If it's still not getting hot with all the other rads turned off I would suggest they are really blocked try tapping them on the cold spots really fast with a rubber mallet or heal of a shoe to dislodge the rubbish it will get picked up in the magna clean or Maybe hire a power flusher
You need to try balancing the system then turn all rads of via the back valve and crack open the working ones quarter or half a turn hopefully you will end up with a good balance