You had the battery off for charging. You install it and this happens. That tells me either your battery is unable to hold much of a charge, its connections to the starter are faulty, or the relay has just plain given up the ghost for some reason. A relay that has done this once is apt to do it again and the same condition could happen with a new one if the reason behind the problem isn't remedied. Charge up the battery again then have it load tested at an auto parts store or do it yourself if you have a suitable multimeter. If the battery and its connections are in good condition, you could clean the relay's contacts and try using it more, or get a replacement.
