How to fix iPhone 4 stuck on Apple startup logo?

My iPhone s kind of beat up and so when I dropped it yesterday, it shut off. Usually when this happens, I just plug it into the charger (my lock button broke) and it turns back on. This time, it kept on staying on the apple startup logo. Every single time I disconnect it, the apple logo disappears and the phone shuts off. I don't want to restore it because I don't have a backup for my phone and I d rather not lose any data. However, this morning, I fixed it somehow by unplugging my phone from the charger and plugging it back in, repeatedly which then caused my phone to stay on the apple logo when I unplugged it. I don't know how to do that again because my phone shut off again after I dropped it again (I know, I keep dropping it).

How could I fix this without a restore?

In most cases, you can solve these problems by putting the phone into recovery mode and restoring it from backup. To do that, follow these instructions:

>> Connect the USB cable that came with your iPhone to your computer, but not to your iPhone.
>> Turn your iPhone off. If the phone won't turn off in the traditional manner, just keep holding the buttons until the screen goes dark.
>> Once you've turned the device off, press the home button on the face of the device and plug in the USB cable to the device's dock connector.
>> When it turns on, keep pressing the home button until the iTunes logo appears on the screen.
>> You'll know the phone is now in recovery mode because a window in iTunes will tell you.
>> You can then start the restore process by clicking the Restore button in the iTunes window.