The inability to shift to the highest gear (smallest sprocket), assuming that the high limit screw is properly set, also raises the possibility of a cable problem. If the cable is snagging either in the housing or at some other "choke point", like a ferrule, the otherwise-perfectly good RD spring may not be strong enough to overcome cable friction, resulting in sluggish/no shifting to the smaller sprockets. I have seen people try to overcome this by reducing cable tension, resulting in screwed-up shifting across the entire cassette. If your cable hasn't seen some love recently, or even if it has, consider pulling it to ensure that it's properly lubed and not rusting or frayed.