Best throw something at it and hope it works is the cable and housing mentioned above, its a semi-regular maintenance item and worth trying. Before trying check the hanger.
Stand behind the bike with it straight up and down and look at the der hanger, the part the rear der bolts to, is it straight up and down. If you can't tell easily either way by looking but the chain in the middle ring in the front and the largest gear in the back and see if the pulley cage is running straight up and down, if it looks bent you may need the hanger straightened. It is a steel frame so this is less likely but can still easily happen and is often shown by the bike not able to drop into the smallest gear as dropping the bike or crashing it often bends the der towards the center. You will need the tool to do the job, a skilled mechanic can eyeball it fairly well on a 7 or 8 speed bike like the trek 800 but it requires the tool to get it best.