Alex, the 1601 error is being treated the same as a 1604. Follow what Apple has to say about it first "This error is often related to USB timing. Try changing USB ports, using a different dock connector to USB cable, and other available USB troubleshooting steps (troubleshooting USB connections. If you are using a dock, bypass it and connect directly to the white Apple USB dock connector cable. If the issue persists on a known-good computer, the device may need service.
If the issue is not resolved by USB isolation troubleshooting, and another computer is not available, try these steps to resolve the issue:
Connect the device to iTunes, confirm that the device is in Recovery Mode. If it's not in Recovery Mode, put it into Recovery Mode.
Restore and wait for the error.
When prompted, click OK.
Close and reopen iTunes while the device remains connected.
The device should now be recognized in Recovery Mode again.
Try to restore again.
If the steps above do not resolve the issue, try restoring using a known-good USB cable, computer, and network connection." from here. I have had a 1601 and 1604 with a bad battery before as well, get one of those from here, as well as many other places, just to make sure. Do make sure that you have a good, and proper, cable. This error really should not interfere with your LCD. Looking at your images, I am not quite convinced that it is the LCD, but I would replace the front display assembly anyhow. Follow this guide and the part is available right here, as well as many other places. While you do that, check all the cables as well as the connectors for any corrosion or damage to the pins. Hope this helps, good luck.