One evening, the screen of my iPhone 3g would no longer rotate. It was working fine that morning.
I haven't updated or installed any applications.
IOS – iPhone 3g (iOS 3.1) screen rotation problem
iosiphonescreen
Related Solutions
Have you tried removing all the songs from the device and just allowing a handful to sync?
Sometimes the tracking database gets in a bad state and cleaning things out lets you know it's safe to sync the whole load again.
iFixit has a great guide about the disassembly of the iphone 5. All courtesy of the pictures goes to them. Step 11 clearly demonstrates the ribbon cables 
.
I highly suspect that you just yanked a little bit too hard on the LCD cable and hence the black screen. I am in no way affiliated with iFixit but I recommend the use of the iSclack opening tool. It only lifts the screen as much as it needs to preventing you from breaking the delicate ribbon cables.
Best Answer
The process in charge of reading the accelerometer may be having troubles. I suggest you hold on your power/suspend button for 5 secs and then completely turn off your iPhone. After the phone has been turned off, press the power button again to start it (this will perform a "cold boot" of the phone). That's the equivalent of completely powering off a computer.
If the problem persists after the reboot, then you might have to restore your phone from a backup using iTunes.
Please provide more information or use the search tool in the upper right corner of the website to find similar answers on how to restore an iPhone from a Backup.