That some work and the the furthest don't does tend to indicate a balancing problem.
Balancing: the water prefers to take the shortest route from the boiler and back again IE through the nearest rads only. What you have to do is partially close the valves on the nearest rads to the boiler so as to force the water on the longer path, to the furthest rads. In simple terms, start with the nearest to the boiler and shut down the valve until you can feel a temperature difference between the water going in and that going out. Then move to the next and repeat - etc etc.
If you're going to say "the water coming out is already cold" then balancing isn't going to help, your problem is something else.
It also sounds like your boiler isn't up to the job. Does it have a thermostat to set the output temperature? Turn it up. As Hamish said, turn your pump up, if you can.