Original iPhone won't start up

It plugs in and the screen lights up to the silver apple, stays on that screen for like 20 seconds then black out. No water damage. Any ideas?

Screen looks like this:

Added (1). How? The image I attached is the only thing I can see/access and it is plugged in but iTunes doesn't recognize it as being plugged in.

Try restoring it

You can get an iphone 4 free right now with a 2 year contract, I would just make the upgrade that way instead of messing with a phone that outdated.

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