How can I restart an iPhone 4S with a broken lock button and frozen springboard?

Go to settings general then accessibility. Turn bold text on and it will reboot your iPhone and fix a springboard crash. I was having the same problem and lucked out and found this!

If you're lucky, you have enabled fast-switching to Assistive touch. Try triple-clicking the Home-button. If there's an option called Assistive Touch popping up, click it and you'll find where you can put it to sleep or power off by holding the lock screen button.

If not, there isn't really any other option. You could try these tips I got at Apple Support Disscussion:

You can squeeze (pinch) the Power Button top corner front glass to the back case while pushing the Power Button and the Power Button will usually function.

If you have jailbroken your iPhone and by chance enabled SSH, you could connect to it and reboot it from there, following this guide.

Barring that, you could run a game or other CPU intensive application like mapping to accelerate the battery drain and get the device to power itself off.

Enable AssistiveTouch: Tap Settings, General, Accessibility, AssistiveTouch (near the bottom) and tap AssistiveTouch to ON.

You will now notice a small dark square with a circle in the middle (you can move this square anywhere). Tap the dark circle to open the AssistiveTouch menu, then tap Device and tap and hold the Lock Screen icon. This will bring up the iPhone's Power-Off slider - no need for a power button any longer!

I saw this when I was trying to figure out how to turn my phone off and it works!