.... I am thinking the battery is not holding any charge.
Try charging overnight with the unit off. The charging circuit looks at the state of the battery before charging. If the battery has a very low voltage, it will trickle charge the battery until it gets to a safe voltage, and then full charge will commence. This trickle charge mode can take several hours, and it is done for safety reasons, and it will appear that the battery is not working as the trickle charge mode takes some time. When in this mode Mojo must be off.
When charging make sure the battery light is white and not flashing - if it flashes, pull out the charging cable, count to ten, re-attach the charging cable. If it continues to flash, it is most likely the charger is not giving 1A at 5V, so use a better charger.
Rob