Like Ajaz said, it is possible. You need a temperature controlled heat gun, set to about 700 DF, and a good metal spudger to create an incision point on the corner of the device, and then about 8-10 guitar picks to slide gently around the perimeter of the digitizer, to de-adhere the glass from the frame. Time is on your side. Take your time, move slowly, and you should be ok.

It's one of two things: it's the digitizer itself (purchased bad digitizer), or it's the actual input connectors on the motherboard, which can (and do) get damaged on DIY attempts. In that case, soldering the new connector on (the new digitizer connector, that is damaged, in this hypothetical) would be the only solution. That's a difficult task.

I agree w/ one of the other posters. You probably had a bad digitizer on this, unless of course, one of the input connectors for the digitizer got damaged during the teardown, when you were removing the old digitizer connectors. If that's the case, soldering a new connector (whichever is broken) onto the board will work, but those are hard to find, and that's a particularly hard job to do.

If you mean that the LCD is damaged, it'll be pretty hard. You will have to remove the digitizer (the glass) from the device, by carefully heating the edges of it, and using precision pry tools to remove the glass. Then, you can order a new LCD, on the web, or from a company like eTechParts (not affiliated), and replace the LCD. In some cases, it's impossible to not break the glass when removing it from the device, in which case you should also purchase an extra piece of glass, to replace the broken glass with. If you are talking just about the glass, and are trying to prevent damaging the rest of the device, watch some iPad air screen repair tutorials, and take your time.

I agree with the answers relating to the backlight. This happens all of the time, from either too much heat (when tearing the iPad down), or damaging some of the connectors on the motherboard that the electric current for the backlight flows through. Happens commonly with DIY attempts which means, if you're DIYing an iPad repair, be MORE CAREFUL than careful. Be neurotic about it.

If a hard reset doesn't work, it may be a backlight problem. The backlight controls the distribution of light throughout the screen. Sometimes, the device can be on, but with nothing visible on the LCD, because the backlight is damaged. If you look at it under a light, you should be able to see very faint images of the iPad home screen (or wherever you're at, on the iPad). Meaning: a broken backlight normally just renders an extremely dim screen, that's almost impossible to see, that people often think is completely dead.