Unfortunately, Apple likes to change just enough during each model year to make it impossible to have everything working if you swap the board with the board of a computer other than the same model. Have you tried having the board water cleaned? Also, especially on MacBook Airs from what I've seen, the keyboard is most likely the issue you're having, not the board itself. Since the power button is built into the keyboard, once the keyboard goes, you usually aren't able to power it on anymore. My suggestion is to try to have the board water cleaned and have the keyboard tested to ensure that's not the problem. But if you're looking to upgrade computers, you may want to just bite the bullet and buy a new one. Hope this helps!
Even if the cracks have been there for months, the digitizer inside the glass is what is finally starting to fail. When you crack the glass, sometimes the digitizer is fine, other times it will fail immediately. My suggestion would be to take the screen to a professional and have it replaced. You'll have all your problems fixed with a new screen.
You can pop the bottom pan off to see if there is any significant water damage. The pan is only held on by ten small Phillips head screws. Omce you take the pan off, you'll see the board, and you should be able to tell if there is obvious corrosion. The connector for the monitor you're talking about is called an LVDS connector. When you take the bottom pan off, turn the laptop around so that the battery is closest to you, and on the top right corner of the board there should be the monitor cable connecting to the board. Look specifically to see if there is any corrosion in that area. If there is, disconnect the battery, discharge the board (hold the power button down for 60 seconds with the battery disconnected), then get some high percentage isopropyl alcohol and a tooth brush to clean out the corrosion. Let it dry, and reconnect it to see if that works. If all else fails, it's possible to see if replacing the LCD or entire lid works, but you'd have to have an extra one laying around to test it. Let us...
The most likely cause is the backlight board. It'll go on for a couple seconds, then essentially get tired and turn off. If it truly is the backlight board, if you look really close right after the screen shuts off (like really super close, and possibly with a flashlight), you'll see a faint outline of the Apple symbol in the middle of the screen. It's an easy enough repair if you have a replacement and the right tools. Other sources of your problem include the actual LCD, and the graphics card. It's harder to test those though unless you have another one you can put in to see if it fixes the issue.
@danj is right, the model should work fine with external storage, especially if the same adapter and thunderbolt cable work on a different mac. It may not work, but resetting you PRAM is worth a shot to see if it'll kick your thunderbolt port back into gear. Shut down the computer, hold down Shift+Command+P+R and press the power button. The computer should start up and chime, then shut off again. I always keep holding the four keys down until it goes through this process four time (just for good measure). Let us know if this works, or if you find another solution!
Most likely the connector came loose when you dropped it, or you damaged the LCD in the fall. You'll have to take it in for repair at a local shop, or get the parts here on ifixit and follow the guide and do it yourself. Make sure you get a digitizer too if you do it yourself. Even if the glass isn't broken, you'll likely destroy it in the removal process.
Your HDMI port is bad. A lot of the PS4s had them go bad. You'll have to take it to a local repair shop. All shops are different on their prices, but you're probably looking at about $99 to have the solder a new one on.
You're going to have to replace the front camera. I know you said the ribbon cable looks fine, but if the front camera and the earpiece isn't working, that's the only common denominator between the two.
Not sure what C Spire is, but if it's a 5S motherboard, then yes, you can use one board in the other phone. All 5S phones have the exact same board in them. Make sure you follow the infix it guide to make sure you don't nick anything during the process!
The Craigslist post was deleted, so I can't open it to see what's going on. From your description though, it sounds like the glass if coming out of the screen? If that's the case, then yes, it's just a simple reglueing of the glass to the lid. On an aluminum MacBook Pro the hinges are almost impossible to break. I've never actually had to replace a hinge on one, so I wouldn't give that too much thought.