Ah...... When you saw nothing from the tube at all, you most likely had the starter disconnected from the circuit (turned counter-clockwise).
What happens normally is that when you switch on there is a complete circuit through the filaments at each end of the tube and the starter. You see the ends of tube glow (normally with a yellow/orange color) and after a couple of seconds the starter breaks the circuit.
That stops the filaments from glowing, but the pulse of power generated by another component inside the fixture when the starter opens causes the tube to strike, and the ionized gas then results in the tube lighting as normal.
Once the light is running, the starter plays no part, and you can actually remove it completely and the light will stay on. If you try to switch on without the starter though, there will be no circuit to heat the filaments and at best you might see a few feeble flickers as the tube tries to strike without the appropriate heat and pulse.
Starters generally fail in two ways: Either they don't complete the circuit when you first switch on, or they fail to break the circuit once the filaments are glowing. In the first case, the light will just sit there as if there was no starter at all.
In the latter case, the filaments will just continue to glow but because the starter never opens the light will not strike. That's when turning the starter to disconnect it by hand will make the light come on, as you are effectively breaking the circuit as the starter should do. If the light just sits there indefinitely with the filaments glowing, then eventually the tube will burn out (which could be what happened to your original tube).
Sometimes as the starter goes intermittently faulty you'll find that the tube strikes, but after a while the starter closes again, extinguishing the tube and heating the filaments again. The light will then often flicker on and off randomly. Again, removing the starter once the tube is lit will allow it to work until it's switched off.