Give the phone a second to charge, it might be that the battery died on you. The phone doesn't power on right away if the battery is fully drained. If you can, take it to a store rather than call tech because it seems like its just the battery. If not they will probably switch it out right then and there. Either way, its faster than dealing with tech support.
I agree, take it into a corporate store. Don't go to an "authorized dealer" as they can't do an immediate replacement in most cases. It does sound like your phone isn't charging. Possibly battery, but more likely your charger has gone bad. In which case your battery could also be bad as well. Take both your phone and charger into the store with you. If the problem is with your charger, replacing the battery alone isn't going to fix your issue.
