Battery Charger Not Working

I recently purchased a cen-tech battery charger, model number 60653 . when i got it home,and plugged it in, it did not turn on so i unplugged it and hooked up the clips to the battery then plugged it back in to a different outlet and it still did not turn on .I checked outlet for power an it was ok . I took the charger back to the store an exchanged it for another charger; same model. when I hooked it up I got the same results! the battery is about 3 years old but has been setting for about 2 years not being started due to needing repair. { clutch replaced } my question is, does the battery half to have some power left in it in order for the battery charger to work. the reason i ask is I hooked up my cen-tech battery booster to the battery for about 10 seconds then switched to the battery charger and the battery charger started working . I set the charger 2 amp for the next 24 hours. hopefully the battery will charge