it sounds like your clutch needs to come apart and be inspected if it suddenly started doing this, or what happened you went to change the clutch cable and now its doing this or? go over your cable installation procedure again paying very close attention to details..
however I do not understand the part about if you pull the lever the clutch will not come back out? how do you know its even actuating at all with the cover on?
there is no way to determine clutch rod action with the cover off so how do you come to this conclusion the rod is not moving?
looking at teh drawing here you can tell that there is no way for the clutch to still be disengaged without the rod disengaging it, #29 and #30 . . .
if #29 and #30 or moving freely I don't see how the clutch can remain disengaged aside from some maladjustment at the clutch itself, if that's even possible, is it slipper?
you may want to clarify "I opened up the inspection cover on the "right" hand side of the bike and the rod moves freely" you then said "After pulling the clutch lever at the handle bar the clutch rod will not come back out" which is it, clarify whats what here, does #30 move freely or not, it should pull out with your fingers if they're not too slippery..
with the sprocket cover off can you pull #30 out? try that, if it moves freely and comes out easily then move on to determining if #29 moves freely by loosening #31 and moving #29 it slightly by using the #30 rod pushing on it from both sides, don't move it more than 1/4" either way you just want to inspect that its not frozen . .
as soon as you remove the sprocket cover your clutch should be 100% engaged, as in the clutch should be in the power transfer mode, like when the lever is out fully.. engaged... in gear spinning the rear wheel forward rotation the pistons should move, you can remove plugs to be sure it will move easier with no compression however I would leave plugs in and get another person and really wrench on that rear tire forward to see if the clutch slips at all, if pistons move with plugs in clutch appears to be engaged fully as it should be...
if your sprocket side clutch rod is frozen clean up area well so its 100% clean, if it still does not move grab a leather belt or a thick hard rubber something and wrap it around the clutch rod and grab with vice grips.. grab away form the seal at least a good inch.. that way if you marr the bar it wont matter in that area, when you get good solid grip on it try to spin it before pulling out, this will unfreeze it, if it spins real easy but still wont come out odds are its bent and that's why it wont come back out, happens.. no biggie, with the vice grips spin and pull till she comes out, try not to mess up seal that one is a bugger so no tools in there and keep vice grips away from the seal . .
if rod is bent you will need a new one..
lets us know how removing #30 goes, roll it on a perfectly flat surface, if its straight but didn't come out easy it may be gummed up inside? rare but possible if maintenance was neglected? spray with a solvent dissolving the gummy area inside the block if that's the case.. be sure everything is working 100% then change oil, if its a fresh oil change then remove that oil before spraying solvent in the crankcase, add old oil then spray that area inside the block till its clean, you may need a scope to inspect properly?