then you have black corrosion sludge in the system. This commonly causes partial or complete blockages. Taking the rads off and flushing them through is a good way to get rid of a lot of the sediment, though not what is in the pipes and boiler. While the rads are off, open each rad valve into a bucket to see if water squirts out or if the pipe is blocked. If you have a sediment problem but not a complete blockage, add a sediment-loosening chemical cleaner such as Sentinel X400 and run the system for 4 weeks before draining and rinsing.
Sludge and sediment are much more common in old, neglected open-vented systems.
But as Agile says, it may be the pump if you are not getting circulation through any of the rads.
If some rads are hot and some cold, turn off the hot ones to try to force flow through the cold ones. However it is possible for Thermal Convection to take heat to the nearest upstairs radiators even if the pump is not working.
Boiler tripping - if you mean it is overheating, suggests lack of flow, might be blockage, failed pump, or short of water
losing pressure suggests a leak. If it is not coming out of the boiler relief pipe, look for damp patches (might be out of sight under the floor) especially under rad valves.
I am not a pro (Agile is, and very expert)