Some thoughts of what I might try , a year on a battery isn't out of normal , especially if you have a problem or if the battery was a cheapie , I would charge the battery over night on a low voltage charger , like 1-2 volts , start the bike , put a multi-meter on the battery and see how dc voltage is being put back into the battery , should be around 13- 14-14.5 , if it passed that test , I'd disconnect the positive cable and put the meters' negative lead on the post of the battery and the positive lead to the cables , should read nothing or very minimal , if it has a draw you would see it , if you do have a draw , you could disconnect plugs one at a time till you find the circuit that it is on ----- you may also have a carb/fuel problem and be fighting two problems and trying to relate the two to one cause