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It depends on how it and the wheelchair are wired and how the voltage is derived.
Presumably the 24 volt wheelchair requirement is provided by two 12 volt batteries connected in series and these could be recharged in series by a 24 volt charger and a pair of wires or by a 12 volt charger providing a 12 - 0 - 12 using three wires where one 12 is a positive in relation to the 0 and the other is a negative in relation to the zero making a potential difference of 24 volts.
There could conceivably be circuitry within the wheelchair that requires only 12 volts for recharging and causes the two batteries to be charged separately, though while this method could be desirable and offer some benefits it would be considered unnecessarily expensive and complicated for most commercial purposes.
As usual you really need to know what is supposed to happen or is designed to happen before fault-finding can begin. One of the wires could be a safety ground wire but most likely it is used to provide some sort of feedback to the charger from, perhaps, a thermal switch close to the batteries so charging will cease if too much heat is generated.
If the charger is lighting up its probably the battery. Rechargable batteries have a lifespan governed by the number of charges. The only sure way of knowing is to have another battery or charger that you know does work. if it is the battery its normally cheaper to buy another complete drill.
If the battery is not damaged or totally dead, you can attempt to charge it with any 24-Volt DC charger. The charging voltage rises to about 28 Volts when nothing is connected to the charger. You must first connect (with jumper leads) the positive charger output to the positive battery terminal. Use a test meter to determine the polarity of the battery. Also test the charger output to determine the polarity. Be sure to connect positive to positive and negative to negative. Do this before turning on the power to the charger. If the battery is a "smart" battery; that is with built-in electronic control circuit, the ordinary charger may not work. Normally, a battery will accept a charge until it is nearly completely charged and then the battery voltage will slowly "buck" the charging voltage. When the battery voltage and the charging voltage are equal, no more charging current will flow. Amperes, that is coulombs of current, charge the battery; when the battery is at (approximately) 24 volts and the charger is putting out 24 volts, NO current flows. The battery is then fully charged.
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