iPhone 4 on reboot loop My iPhone shut down, and asked me to restore and update, which I think means that it's going to delete all my data, which I'm nervous I won't be able to get back. 

After that, I haven't been able restore it.

I plugged it into the charger, and the Apple logo pops up for 5-8 minutes, then it vibrates and turns off, in a loop.
I plugged my iPhone into a laptop, to try and back it up, then restore it on iTunes, but it wouldn't go to the screen that told me to attach to iTunes anymore. 

My sleep/wake button is broken. So I can't reboot it.

I got it plugged in iTunes, and it kept saying "unknown error" and now it's not getting past that.
You could get it into restore mode by holding the home button while it boots. So turn it off if you can, or wait for it to turn off. Then while plugging it in, press and hold the home button.