Welcome to Android Central! I agree -- if the battery has drained completely, you may have to let it charge for a few hours before trying to power on again.
The G2 is a pretty old phone with a non-removable battery, so the battery itself is presumably old as well. Batteries degrade with age, and are more prone to sudden discharge, especially under increased stress (hence the whole hubbub over Apple's throttling of iPhone speed as the battery aged -- it was to prevent this kind of thing from happening). Chances are that the phone needs a new battery (or your wife needs a new phone).