When you click on links to various merchants on this site and make a purchase, this can result in this site earning a commission. Affiliate programs and affiliations include, but are not limited to, the eBay Partner Network.
Did you disconnect any wiring from the starter when replacing the battery?
Sounds like the positive lead from the battery is now directly connected to the motor terminal of the starter instead of the switched terminal controlled by the signal wire coming from the ignition.
Wire three and wire four are touching. Wire four is battery + and wire three is start signal from the key. Don’t forget to connect wire three to the same post as wire four per this diagram.