Why does the backlight work but nothing else?

I dropped my iPhone 4s on the tile at work but it worked perfectly after that. When I got home I took it out if it's case and noticed the back glass was badly cracked. I was upset but the camera and flash worked fine. I even got texts from my friend but minutes later I look at it and the apple logo was on. It stayed that way for a good ten minutes before blacking out. The screen light stays on but with no image and that's it. It doesn't make a sound when being charged, put on silent, or getting a notification. I can't turn it off or on and when I tried to hard reset it it'd turn off for a second, return to the apple logo for it bit then return to the backlight with no image. Sometimes when to apple logo comes on computer like code pops up at the top saying things like checking borrowed blocks, FIL_Init [ok], VFL_Open [ok], and _FindFlashMediaAndKeepout : 601 physical nand block offset 1 even error unclean shutdown; adopted 26791 spans. It just popped up as a black screen with a white line down the middle. I tried searching on google but I couldn't find anything. My computer broke down a couple days ago so I can't use it for iTunes sync and such. Is there anyway to fix it because I just bought it. No warranty or AppleCare either.