if its an old cable it might have stretched after a million gear changes?and not quite give the stroke it needs,now its snapped it might be why?see what its like with the new cable,you might drop the clutch cover,dissemble/inspect and reassemble the clutch and it might come good?the thrust washer at the basket might be worn?expands with heat and takes up slack maybe?,with total cable slack the notches on the case and arm should line up as you lift the arm by hand into the declutch position,try adjusting it one way then the other as you watch the marks come close and apart,stop and lock the nut when you think its on the dot,have the handle bar end about two or three threads out,then take up slack at the bottom end of the cable,work the lever from time to time to settle the cable as you do it,see how it is and adjust further at the handle bar end if needed,the adjusters at each end of the cable do the same job,the handle bar end needs no tools though and is used for on the go adjustments,you should be able to pull the outer say half a millimeter from the adjuster at the handle bar end,a dragging clutch is a real pain,is the cable routed correctly?