I don’t think the above connector from Aliexpress is correct. Looking into it it seems to use the same connector that is on the Samsung Galaxy Note 4 2014. It is actually a 70 pin connector not 35 because there are pins on both sides. You might be able to buy a replacement off eBay or Aliexpress. Below is the link to the connector on Aliexpress. FPC Connector From Aliexpress
It sounds like you might have an issue with the backlight if the phone is working but you just can't see anything on the screen. Try shining a torch on the screen and see if you can see a faint image. It is possible you may have damaged a component associated with this as they are around where you plug in the connectors. You can also damage components that would give no image at all. You tend to get the "boing" noise when you plug in the charger with no screen connected.
The most likely cause will be the screen but if after replacing it you are still having issues it could be a problem with a Touch IC chip on the board. This can be reballed or replaced to fix the issue.
No. If you replace it you will get error 53 when you try and update your phone. The original touch id home button is tied to your motherboard. You could try cleaning the connectors for the home button and see if that helps. There is the one on the motherboard and then other is on the flex by the home button. Just use some isopropyl alcohol and tootothbrush/cotton wool bud and give them a gentle scrub. The water damage may have left some deposit/corrosion that is causing them not to function properly.
It is pretty common for this part to become faulty if it gets wet. You need to replace the board shown on step 21 of the teardown. Samsung Galaxy S4 Teardown It is quite cheap to get hold off. http://www.ebay.co.uk/itm/USB-Charging-Dock-Port-Flex-Cable-with-Mic-for-Samsung-Galaxy-S4-I9505-REV25-/111764568601?hash=item1a05affa19
This can be replaced here is the part I think you probably need. http://www.ebay.co.uk/itm/UK-REPLACEMENT-Acer-Liquid-E3-E380-GLASS-DIGITIZER-TOUCH-SCREEN-4-7-LENS-PARTS-/151750074325?hash=item2355025fd5
First try changing the battery. Quite often with water damage the battery can become faulty. If you haven't already you should also clean the motherboard of all traces of water. The are lots of ways to do this but the easiest for you would probably getting some isopropyl alcohol and brushing all visible signs of corrosion with a toothbrush. The screen may have also been damaged so that might need changing. First try cleaning and changing the battery.