As these machines have to run at crazy angles, they do not have a typical carburettor with a float bowl - therefore they have to pump their fuel from the tank continuously.
When you press the primer bulb, you are manually pumping fuel from the tank - on starting the engine is supposed to take over.
So, if you want to have a go, you'll really need an air line (but an aerosol can of carb cleaner may suffice) and the carb will have to be unbolted.
On each end of the carb there is a squarish plate - unscrew these and underneath you'll see a rubberised diaphragm.....one will have a round metal disc in the middle, and this is called the metering diaphragm.
The other one will have some U shaped rubber flaps - this is the pump diaphragm and the fault will be in the drilled passages leading to this.
These diaphragms are fragile, and mustn't be torn.
Basically, every part needs to come out of the carb for a clean - a bit daunting but not so bad if you carefully keep the bits in order.
Anyway....here's a few tips to try.
Does the engine keep running so long as you press the primer?
Does using half choke help? Try starting (if possible) with full throttle and choke off.
If there are two screws in the side (maybe marked L and H) turn them in, and then out one turn.
If you think the thing may be drowned in fuel, take the plug out, tip the machine over (plug hole downwards) and pull the starter cord to clear any raw fuel away.
Sadly, getting parts for this Chinese stuff is nearly impossible unless the importer will help....and most horticultural repairers won't want to know.
John