The battery light is really simple Kez, its located between the battery and alternator. It extinguishes when the battery voltage and alternator voltage are balanced (14v charging give or take) as the power can't go anywhere. When the alt stops producing enough charge, the battery voltage is higher, and passes back to the alternator to balance the circuit, putting voltage through the batt light so it lights up. As your old batt was low on charge, the voltage between that and a dying alternator were both low but even. Put a new batt on and it shows the alternator fault!
Its most often the alt or battery at fault, but can of course be earth points or connections aswell.
Its most often the alt or battery at fault, but can of course be earth points or connections aswell.