John, take a good close look at that bike.  If it does not have an H-D on the side, it probably isn't worth fixing.

But rather than have you walk away disgusted with my Harley attitude (which I like) here is the remedy.

1.  Check the play of that new cable.  If you have less than 1/4" of free play before you feel the clutch move, then the cable is too tight.  Loosen it so that it will actually engage.
2.  If the cable is adjusted correctly, but the clutch still won't engage, go through all the steps needed to pull the side plate and pull the clutch.  Kawasaki is infamous for inconsistency: some models have a dry clutch, some have a wet clutch. 

If the clutch is in the engine cases, then it is doubtless supposed to be wet.  If a wet clutch goes dry, it will glaze and you go nowhere. 

If it is in a separate compartment, it is supposed to be dry, and if it gets oil on it, it will slip instead of engage.  Either way, replace the clutch.

While you're replacing the clutch on that efeminate little Kawasaki, think about replacing the rest of that rolling wreck with a MOTORCYCLE!

It is easy to tell.  It will have H-D on the side, and that doesn't mean Honda.