To get your landlady interested, point out that the radiators are filled with moist, warm air, and that the system is corroding from the inside, shortening the life of the radiators and clogging the boiler with rust. That means the boiler's life is being drastically shortened and may soon cause a massive expense. Fixing it now would be much cheaper than fixing it later. The question is, is she greedier than she is lazy?
As to what's actually the problem?
It seems to me that your apartment's system wasn't being replenished with water. Opening the radiator bleed valve wasn't doing anything because there was no additional water available to replace the air.
Central heating systems come in two flavours -- open vented and sealed -- and each refills with water in a different way. In an open-vented system, there is a tank at the highest point in the system, that uses a ballcock to fill up with water: see this diagram at diydata.com. The ballcock is in the feed and expansion tank. If the ballcock isn't operating correctly, the feed and expansion tank doesn't fill with water, and so no extra water will be available to fill your radiator. The ballcock could be stuck, or it could have been tied off so that some work could be done, and never untied. If you've got that kind of system, the fix would be to get the ballcock moving freely again. Is there some kind of maintenance area you could check out?
Alternatively, it may be a sealed system; there's another diagram showing that. These systems are filled up with a tap -- see the 'filling stop cock' in the other diagram. Normally, you'd check the pressure in the system every few months and use the filling stop cock to make sure the pressure is high enough -- say, 2 to 3 bar. Again, this will probably be very close to the boiler itself and so would need access to your building's maintenance area.
My guess is that it's a sealed system, and that the internal pressure has dropped right down to atmospheric pressure on the fifth floor. Lower apartments won't be suffering because gravity gives them more than their fair share of water, so most tenants won't suffer. However, any rust generated in your radiator will sink down into the system and clog it for everyone.
It maybe that air got into the system and this is preventing the heating system to fill up properly. You may have to remove the air from the boiler itself, there should be a valve to enable you to do this. Replacing the pump seems to be either coincidental or unecessary. Also, when draing some or all of the radiators down it is advisable to put a chemical in to prevent any corrosive effect from taking place. This may have a minimal bearing on how hot the rads get, clean water in the system can encourage furring to take place and therby reduce the pipe thickness, again preventing enough water through to the rad.
Lastly, if the rad or system is old, you may have some thick sludge which will prevent the pipes and/or rad from getting any hot or cold water at all. depends on how thick the sludge is. The sludge could have been disturbed when the system was drained down.
To remove the sludge you can buy a chemical remover and put it into the rad which is worst effected and turn the heat on, then most suppliers recommend you drain the system and put a chemical in to prevent this again. Finally, I had to hit one rad because it was located in a room where i could not get to the valves. I kept on tapping it with a hammer to encourage the sludge to move on and into the outflow, with patience this did work but it did take 30 -40 minutes of tapping and bleeding.
Best Answer
Every bleeder. Some may not even be on radiators (depends on system layout/design - bleeder elbows are common, but more on baseboard than radiator type systems.
If there is air trapped in a radiator, no water gets pumped through it. Circulator pumps are very limited devices. They don't do well at pushing air bubbles around the loop.