OK kovertk. So far so good. If you open the screw marked "P" on the fuel pump you get just a low flow with some bubbles of air? Normally you get this when the pump is stationary and, for instance, a new flexible fuel hose has been fitted. (This is where we connect in our fuel pressure test gauge / combined bleed manifold by the way.) The next step is to put loads of kitchen paper and perhaps an old oven tin, under the "P" port and switch on the boiler. Get an assistant to help, as when the fuel comes through, you scream and your assistant switches the boiler off. That's the fuel system bled of air. However, if you only getting this low flow etc with the pump / motor / fan already turning and you know that you have a good oil supply to the pump, you are correct to be looking at the solenoid.
Most that I have come across are"mains operated" i.e. 220 volts ac. What type of burner have you got? We need to find out about this 16volts.
Sometimes you can tell that the solenoid is producing a magnetic field by holding a (NON-MAGNETISED!) steel screwdriver over the end of the solenoid that is facing away from the pump. Switch on and you should feel the solenoid pulling on your screwdriver. Another way is to remove the solenoid from the pump, hold a small screwdriver in the centre of the solenoid and see if, when the motor runs, that a magnetic field attempts to hold the screwdriver in place.
If of course the solenoid is a mains operated one, which is why we need to know the burner make / model etc and you only have 16v then check all the electrical connections via the control unit. If the control unit has 220v ac going in and should be outputting 220 v ac to the solenoid and isn't, then it is the control box. I'll watch this post for the latest episode.