Will I lose my photo's or can I still save them

I need to restore my phone because my comp says its corrupt. I have 800 photos/videos I CAN"T put on my laptop becaue of it being corrup. I don't want to lose these photos, they are of my daughter. Most of them are not on my laptop nor facebook. If I backed it up to my laptop or iCloud would I be able to save them. Most of them are not in the photo stream. I don't care about the apps or music, thats all in my itunes library, I just need a way to save them or put them back on my phone once its restored. Is there a safe/easy way I can do it without losing any of my pictures and without downloading some software or something from the internet?

And how do iphone's become corrupt. I have an iPHone 4 btw and it doens't have iOS6 yet.