There is one other thing you might check. In case the previous owner had been experimenting with the mixture, look at the carburetor. There will usually be 2 mixture screws (brass screws with a spring under the slotted head, side by side, going into the carburetor body - not the idle speed screw, which holds the throttle butterfly slightly open). With a screwdriver, turn each of them clockwise gently, carefully noting how far they turn before they stop. Don't use force, they are delicate. You will probably find they both rotate about one and a quarter turns. If so, put them back exactly where they were. If they are open less than one and a quarter turns (i.e. leaner mixture than normal), that may be a problem. If they are open more than that (i.e. richer) don't worry for now, just put them back where they were.
