The "Accessory" message can be due to a dirty dock port on the iPhone, clean it with a clean dry toothbrush. You may also want to use another USB cable.
Charge the iPhone with the Wall Charger for at least 1 hour. It may start-up on its own, which would be good. After 1 hour, see if the iPhone is working, push the home or power button quickly. If no response, keep on charger and try a Reset, hold both Home and Power buttons until the iPhone starts up, usually less than 20 seconds. If no response, Hold down Home button as you connect it to iTunes, keep holding home button until iPhone is recognised by iTunes in Recovery Mode. Then Restore the Firmware. If there are any errors, take your time and write them down. Hopefully this will work. If not, your battery may be bad or something worse.