It's not about options so much as following the checklist to find the cause.

Step one is to make sure it isn't a cable issue. Cables bear close inspection since they can suffer from any number of subtle problems. If you practise your google fu it should be easy enough to find some troubleshooting resources.

You say you've eliminated the derailleur as a possible cause, which if true, and the cable's fine, leaves the shifter. If so, you could try flushing it with WD40 and then some spray lube.