Did my iphone 3gs battery die?

I have an iphone 3gs I want to get hooked up for my little sister to use as an iPod touch. I woke up one day, and the phone wouldnt turn back on. It wasn't plugged in or hot, so I'm thinking the battery died? Is there anyway to know if its the battery. I could just get that replaces.
If I plug it into the computer or a charger nothing happens with it.
I think it's the battery, is there anyway to tell for sure?

Not Necesaarily, it may be a software crash, you can't make sure because the battery is built-in i guess you should pay a visit to the technical support

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