Many questions...
How old is the battery, have you done a voltage test on it, have you done a load test on it?
If your battery has been completely discharged a few times, it's probably toast, and not holding a charge. A good battery should be around 12.6V when sitting at rest, not on the charger. If you're way below that, either it's a bad battery or bad charging system.
The size of the battery wouldn't matter in this case, it's all depended on what voltage/amperage it can deliver.
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