||There are also wires around that area too besides the main battery cables. If someone else installed the battery, there is a high probability they dropped it in and could of pinched/damaged the wires insulation letting them short together.
They also could have let a tool touch the positive side or something and fried a circuit else where but that would be extreme.
Since this all started after a battery replacement, thoroughly check those wires. Damage would be hidden under the loom. Also try a different battery.