Make sure you know the status of the timing belt. The manufacturer recommends changing it at 110,000 miles. 60,000 miles if driven in cold weather. That is an interference type engine. If the belt breaks, the valves crash into the pistons and you will need an engine job.- or junk the car. The belt is relatively cheap. It is the labor that will cost you. Usually when you are replacing the belt you change the, blah, blah, blah. Look at the manual. If you take it to an authorized Honda dealer it will end up costing $500 to $1000 by the time you get out of there. I do not have info on your specific battery. But if it was driven in a cold climate it would be safe to assume it is on its last legs.