Hopefully your problem isn't too bad.  I hate that back ribbon cable setup.  I really wish there was a way to get rid of it & use connectors instead.

One of mine recently black-screened also... I'll have to give that a try.

I think the singe on the ribbon is not the problem, as long as the thin ribbon wires are not snapped/broken and the burn is not on the connector end.
I added a white LEDx3 backlight to a PIL DMG not too long ago, and the DMG had been working fine before I started modding it, but after I put in the backlight, I would turn on the DMG and the backlight would turn on, the sound would work, but nothing displayed on the LCD except a big black square. I tinkered around with different resistors and different methods of wiring the backlight to the DMG, but none fixed the problem. Then someone (probably Kitsch) suggested changing the caps to fix that problem, because the caps eventually die out especially on the older models. Even if that isn't the problem, changing the caps is still a good idea to prevent the DMG from having any problems in the future.

The singe on the ribbon is exceptionally minute. But the thing that I don't get is that it was in perfect working order before I put in the backlight, might I have shorted it out to have to replace the capacitors? Bear with me folks I've never worked with electronics before and am trying to understand.

A tiny burn like that shouldn't matter. If you dug in enough to break a wire you're in trouble.

I think Boddah's suggestion of changing the caps is worth exploring, especially if this is a grey gameboy. What's the board revision (look through the hole where the battery cover latch locks in and there's a part # on the back PCB)?

I don't think the ribbon cable is easily fixable, unfortunately... I'd say your best bet would be to swap the whole front PCB with a new one.

Yep, as I was putting my DMG back together I noticed I had touched the edge of the white back ribbon with my soldering iron and singed it just a little tiny bit, I would like to try and replace it if you have any advice or referrals on how to do this would be greatly appreciated.

Yeah I double checked the website. It's built in.
Well I'm thinking it's that bloody back ribbon i messed with.
Thanks for all you input and taking the time to help a girl out, I appreciate it.

^ yep, the film is built in on the LEDx3 type.  if you got a RGBbb, it was loose in the baggy

Ah I was thinking of the backlights from Nonfinite. I didn't read you got yours from Kitsch. I've actually never bought backlights from him, I'm guessing the film is built into his then.

Well that might be the issue as I didn't receive any such film. Is it usually loose? Because there is a dark gold layer on the back light.

You gotta be super careful with that back ribbon cable my friend.. Also there should have been a darkish, square shaped piece of film that came with your backlight, it goes in between the backlight and the glass panel. afik, you need polarizing film to see anything in an LCD.

Also the Gameboy is in fantastic condition and worked well before I buggered it all up.

Contrast wheel does change the screen, but not alot though.
New polarization film? I'm not too sure what that is.....
The back ribbon cable was bent while I was trying to reinsert.
I'm a bit of a gorilla with electronics.

Try replacing the capacitors, I had the same problem a while back and swapping out all of the capacitors with one of Kitsch's kits fixed it.