iPhone 3G dead and unresponsive to charger and buttons
You could attempt to put the iPhone in DFU Mode, and see if you can restore from iTunes. But this is almost certainly a hardware problem, and will require a trip to an Apple Store or a service provider.

To try DFU mode (note that this does a complete wipe, you'll have to rely on whatever backups you made previously):


Plug the phone into your computer.
Turn it off.
Hold the sleep/wake and home buttons for 10 seconds.
After 10 seconds, release the sleep/wake button, but keep holding the home button.


If this is successful, you should get an iTunes popup stating that it has detected an iPhone in recovery mode. You can then follow the iTunes instructions to restore the software.