Power problem with iPhone 4?

My iPhone has been dropped and I can't turn it on via the sleep button. When I plug it into a wall charger it turns on and tells me to connect with iTunes, but when I connect it to my laptop it does not turn on. It simply shows the iTunes logo off and on without powering up. I can't do a hard reset as my home button is broken. Help?

Added (1). There's no Apple Store in Aruba, where I live

You have 2options.
Get it to a apple store.
Or try as much as you can to drain the battery. After the battery empties. Then connect to laptop turn on iTunes. Let it charge and it should then work fine if not try option 1.

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