Lets put the battery issue aside for the moment. A Nuvi should power up as soon as the charger is plugged into it. It will turn on even if the battery has been removed. Of course, once you remove the charger, the unit will die immediately because the battery has been removed.
The first thing I would suggest doing is trying a reset. There are 2 ways to reset a Nuvi 2xx or 2xxW.
On some units (earlier versions), there is a flap on the bottom of the unit that you press in momentarily to reset the unit. There will be a label on the bottom with the units serial number and the word "reset" on the label.
The other method (newer versions) is to slide the on/off power switch to the left and hold it for at least 10 seconds.
Another common problem with these units are loose/broken connections on the rear USB port. There are 5 pins on this port. If the power pins are loose/broken, the unit will not be able to charge the battery. The unit will not turn on because the battery is dead. Even if you plug in the charger, there battery will not charge.
The unit will not charge the battery if it won't turn on.
More information can be found here:http://www.sharc.net/discus/messages/6/313.html?1338221806http://www.sharc.net/gps_battery_repair.htmhttp://www.sharc.net/gps_charger_repair.htm