Pug: Thanks for your reply.
I bought this bicycle used about two weeks ago, so I don't know when the cables were last changed. However, it has been maintained pretty well, so I think the cables are still in good condition.
The top of the shifter reads: "Shimano Total Integration ST-M020". The derailleur only has the Shimano brand name printed, but no model.
As for the pictures, they should be below. I apologize for the bad quality.
Derailleur:
Shifter:
Andrew: Thanks a lot for the advice. I'll try cleaning the internals of the shifter tomorrow, and let you know if that solved anything. I don't think my local bicycle mechanic is willing to assess my problem without cost. The prices he charges depend largely on his mood. Unfortunately he's the only bicycle mechanic around.