The ThinkPad Edge E220s and E420s contain a built in battery pack. To prevent a deep discharge condition from occuring, the system is designed to automatically disconnect the battery if it is not powered on for two weeks or more.
It is possible that systems sold through resale channels could be in inventory for two weeks or more, and so if a new system won't power up this is a probably cause.
If an E220s or E420s is not used for an extended period of time (threshold is 2 weeks), and the battery has less than 50% charge, then the unit will go into “Storage Mode”. The battery will be disconnected electrically from the system.
When the user starts using the system again, they will need to reconnect AC power to turn on the system. This will help to optimize the battery life.