iPod touch 4g won't turn on, charge, or be recognized by computer

So I have an Ipod that my sister needs help with and it will will not charge (no charging logo), will not turn on, and is not showing up on my Itunes so that i can reset it to factory settings.

I've tried the whole holding down the power button and home button thing (many ways and many times) over and over and it isn't working. The screen remains black no matter what i do. I've even tried letting it charge for a while. I know it's not my cord because my own ipod works just fine with it.

One time my ipod did this but the apple logo would actually show up, turn off, show up again over and over and i was able to somehow restore it to factory settings and now its just fine.

I've seen many questions and answer relating to holding down the home and power button but that isn't working for this situation at the moment. I don't know what else i can do for her ipod or if there is another way to restore it myself or if they need to have it taken in somewhere. Please help. Thanks.