Just a guess, but the possibility exists because they're used, and they're not working?

As the others have said, make sure that the cable heads are properly seated. May want to browse to http://techdocs.shimano.com and grab the setup instructions. Problem with the STI's is they're pretty much non-serviceable, short of some cleaning you can't get parts for them. Once inoperable, if a ggod cleaning doesn't fix them you're pretty much replacing. Since the right shifter gets used more often it's usually the first to go.