Couple of things spring to mind, quality and durability are somewhat lower generally on these machines, so componant failure isn't uncommon.
How old is it ?
standard check list;
battery/ you say is fine
solenoid/ makes a clicking noise
startermotor given a direct feed from + on battery/ does it turn ?
remove starter from bike, from a battery - (earth the outer casing) & + the terminal on top/ does it turn ?
I'll make a presumtion here it's probably a clone of a
denso one, so on the startermotor (removed from the bike) two bolts will run the length of it (internally) undo these, take off the end cap, then you'll be able to extract the central part (
armature), looking down the inside of the casing you'll see a round or half round small circuit board with the brushes attached, you should be able to seperate the main body from the other end cap with the circuit board in now, three things to check here 1. check the brushes are in good condition, 2. the contacts at the base of the armature are also good, 3. the electrical contact from the outside terminal(+ postive) is isolated from the body of the startermotor (undo the 10mm nut on the outside terminal, the bolt bit should go threw an isolator of some kind, either rubber or plastic, stopping it touching the main body (which is obviously the - (earth)), and to a wire or braid which in turn leads to the circuit board, if either the isolator or wire/braid is broken it won't work, it's possible to re solder the wire/braid, and should it be the isolator a piece of innertube rubber cut to shape will do the job.
HTH
Edit: found
this which might help.
Cheers Mark.