Broken iPhone Button

Do you mean the physical home button or the software App Store button?

If its the physical home button:
how long ago did you buy the phone. If less than a year, a repair is free. If its over that, then they'll probably charge you more than you can upgrade to the 3G phone for (depending on your location).

If its the App Store:
Just restore your phone.

 

Book an appointment with your nearest Genius Bar.

If they find the issue to be unacceptable, they will replace your phone on the spot dependent on stock levels.

R-Fly

 

Your problem sounds more like a software problem, restore it first and see if that solves it. From what I am reading it looks like your Iphone software is lagging.

 

Need help

I have an iPhone 3G and i have never dropped it and never hurt it in any way but when I flip the switch on my phone to make it in silent mode that doesn't work the silver thing under it to change my volume fell off the power button on the top doesn't work at all and u have to jam the home button down for 3 seconds before it works and I need it fixed I still have another year on my contract and I can't spend any money if I went to apple would it cost anything to fix it? Or would they give me a new iPhone free?