Q: I left my ipod for a month without recharging it. It doesn't charge at all and shows no sign. How can I resolve that problem?

If you have plugged it into the wall socket charger and left it for at least a few hours - then it is likely a ruined battery.  Lithium cells do not recover from a true, complete power drain.  If left that long, and depending on how much charge it had to begin with as well as how many cycles alread on it, it may have drained to nothing.  If that has happened, it will almost certainly never take a charge again.

Take it into Apple for a free check - if the battery is shot, you can pay for a replacement right there.