The underpowered charger would only keep it from charging when you were using the machine, but it will charge in sleep mode.
To go from from one green to four in an hour is kind of quick for a full charge though, something is odd. If you have battery power it should start even with an underpowered charger.
Is this a MacBook Pro or MacBook? You mentioned a MacBook in your last thread. The MB has a DC in board, it could be that if you're lucky but it does charge so I doubt that. If it's MBP I don't think they have DC in board, it's on the logic board I believe.
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