I agree with Mitch's answer. You may also have a slightly disconnected Lcd, which disconnecting and reconnecting the lcd ribbon from both the logic board and the screen itself will likely resolve. The real challenge though is taking your digitizer off without breaking it, the volume/power ribbon, Wifi antenna, etc.
Try doing a hard reset by holding sleep and home for up to 10 seconds. If that doesn't bring it back, then it could simply be a loose LCD ribbon. Take off the back cover. Disconnect the battery which is held by one ore two screws depending on your iphone, then remove the very top EMI shield. Should be 4-5 screws. There should be two large ribbons to the right of the camera. Disconnect and reconnect. Reconnect battery and turn on the iPhone. If it still doesn't illuminate, disconnect the battery again and disconnect and reconnect other ribbons underneath the other EMI shields. If the LCD still fails to illuminate, then it's possible your LCD is damaged and will require replacement at that point. Best of luck.
The electronic switch is the same for Gen 2 and 3. I'd say that all three of the current generations share the same adhered mounting brackets and home buttons. Only the 4 uses a ribbon because the new port isn't "wide" enough to contact previous Gen electronic switches.
I don't know for sure but possibly your phone is locked up. Might have to pop the back off and disconnect the battery. Reconnect and then plug it into the wall. That should reset it if your sleep button isn't working.
The wifi antenna is along the bottom frame toward the right. Sits between Digitizer and frame. The 4G antenna and GPS are at the top, also slightly adhered to the digitizer. If you look on the back, you'll notice black bars at the top of the ipad, that's where they are housed.
Very interesting, do you have another digitizer to try? If you don't, then you can try cleaning the contact with some alcohol, but I assume you did that. Make sure the ribbon didn't get pinched while closing it up. Latches closed down I assume. Could be a bad digitizer, could be a silly error during install. Best to tear it down and check again. Good luck.
I actually avoid replacing the entire ribbon nowadays just for this simple fact. What I do is replace the orange film with the black nub now. I take it off a new one and place it on the old one. You can't find the film with the black nubs by themselves unfortunately but that's okay. Just throw away the part you don't use. (side note, clean off the surface so the new film will stick better.)
There's a possibility one of the ribbons came loose, even just slightly. Try removing some of the metal shields (carefully organize all the screws) and disconnect and reconnect the connectors. There are directions here on how to do it. Also be careful not to get any skin oil onto the exposed connectors. If that doesn't work... then possibly a part on the motherboard has become damaged. Best of luck.