What is this knob on this fluorescent light fitting?
That component is called the starter. its a really inexpensive component that regulary fails on florescent lights. to remove you turn 1/4 rotations left and pull out. to check that its in turn right until it stops whilst pressing. 



Any good lighting store will have replacement starters for your light. 

Otherwise the things to check would be. 


check that the florescent is clicked in correctly, you will see that if the pins of the tube arent touching the contacts in the fitting it will not turn on. i.e. you need to rotate the tube so that the gold pins at the end of the tube sit horizontal with the ceiling. 
check if there is corrosion on the pins of the tube
remove the tube (turn off light switch), then remove the backing plate look inside for wires that have been detached. the chinese lights I know have really weak connectors and the connectors are always failing