Screen lights up with no image after repair

My iPhone 4's home button was unresponsive so I opened my phone up and tried to replace it. I dismantled the phone a few times but still couldn't fix it.

On my last try, when I tried to switch on the phone, the apple logo didn't come up. However, it appears that the phone is still working as I can still hear the alerts and connect it to iTunes, and the backlight lights up when I press the lock button, just that there is no image, just a blank screen.

I googled for a solution and some with the same problem mentioned doing a hard reset which I can't do now without a working home button, so I am just unplugging the battery for now.

Do you guys think I might have damaged the screen cables while fixing my phone? Or is it just a software issue?

I went to a repair shop and hearing my description they just suggested I replace the whole screen which is much more expensive. Should I do the repair?