i'd guess, and have seen, the shift star and/or the shift detent on the end of the shift shaft on that side, to be the cause of not shifting, way more than bent shift forks, which these bikes are not known for.
if the detent isn't returning to it's nuetral position, it will not shift up or down to the next gear.
after shifting try physically moving the shifter the opposite way your trying to shift to put it back to it's nuetral position, if that works, a new/used shift shaft should fix it.
also check the screw holding the star in place, if it's not the welded type, if it's loose the shift star may be getting cocked and not rotating