If you’ve got some general electrical knowledge, do the following: Get a voltmeter and check the voltage on the battery, check the voltage on the connectors on the starter as well (whilst pressing the starter button, -watch out so you don’t get a chock though)
Generally when the starter only turns the engine round for a short while or only a couple of turns, it means it doesn’t get enough juice (which I’m sure you’ve figured out). This could either relate to a bad battery or bad contact between connectors somewhere in the wiring. If it happened a couple of days after the replaced the wiring chances are that they didn’t tighten the connectors enough.
To avoid future corrosion, slab on some vaseline or silicone grease on battery poles and connectors.