The rear derailleur. Mechanically they are quite simple things, with the clever stuff being done by the shifters. Assuming shifters and cables are working as they should, I would be removing the derailleur and giving it a thorough clean. My way of doing this is a small plastic container with enough diesel in it to give the derailleur a good soaking. Take the jockey wheels off, noting which one is top and which is bottom for re-assembly. It's a mucky job to do right, but use an old toothbrush and give the whole thing a good clean. After the diesel wash, give it another clean in hot soapy water. Re-assemble and lubricate, and I would be surprised if it didn't work as new. Only possible worn bits are as someone previously posted, the jockey wheels. But at 4500 miles I would be surprised... but then I am very surprised that the chain rings are worn at that mileage.