How to fix bricked iPhone 3GS with broken home button?

My iPhone 3GS is bricked where the it would not turn on, connect to my computer or detect on itunes or even charge. It just shows the Apple logo then shuts off when charging. I can't get it to DFU mode since the home button is broken, so I need to know how to get it to boot up again.

The answer to that is to buy a new one.
apples products are designed so that when part of a phone breaks, like the home button, there's no fix. How do you think they keep making money? The only replace-able part of an iphone is the screen. And thats the way apple wants it to be.

Take it to the Apple store, and see if they can get it replaced. And contrary to the belief of what some people think, the reason why broken parts of an Apple device not able to be fixed is not because they want to make money. It's because they believe in end-to-end integration. Also, read this article if you have time. Http://www.macobserver.com/tmo/article/tim-cook-soundly-rejects-politics-of-the-ncppr-suggests-group-sell-apples-s