You should be able to. I found a replacement set here, but no guarantee on part quality or ease of replacement. Also, this part doesn't include the CCD or lens housing either, so make sure you get all the parts you need. There are a few more options out there, but this one is pretty inexpensive. Have fun, and I hope you successfully fix it!

Yes, it is compatible. All the 4th gen models use the same screen.

Was your phone still on while doing the repair? This could have caused the smoke, but hopefully not permanent damage. Always remember to fully power down the device you're fixing. First things first, double check your work. Go back, and look over what you repaired. Your screen could be malfunctioning because of something simple. Disconnect and reconnect the LCD and digitizer, and make sure nothing is pinched, broken, or disconnected. If the problem persists, I would be inclined to say back up your device and replace the board. I'm not entirely sure why the board would be smoking, but it likely isn't easily repairable. Let me know what happens! I'm interested in why the board was smoking. Jordan