Jailbreak iPhone 4 on iOS 4.3.5 with Unresponsive Home Button

Hello Marco, unfortunately, since you are on iOS 4.3.5, you will need working Home button in order to jailbreak your iOS device as you will need to put your iPhone in DFU mode first. On the other hand, for iPhone, iPad, and iPod touch users who are still on iOS 4.3.3, they will be able to jailbreak their iDevices without putting their devices in DFU mode using JailbreakMe 3.0 – A one-click web-based untethered jailbreak solution.

For the mean time, you can download and install a jailbreak app called Gesturizer from Cydia Store. With Gesturizer, you will be able to able to control an app using multi-touch gestures – which are fully customizable and serves as a quick shortcut to your favorite apps. You can check this blog post to know more about Gesturizer app.

Anyway, I would still recommend you to restore (make sure that you backup your device before restoring) your iPhone to the stock iOS 4.3.5 and get a warranty fix or hardware replacement from Apple Store or AT&T so that you can maximize the usage of your iOS device. Who knows, maybe you could get untethered jailbreak on iOS 5?