I find it very strange that an update encrypted your phone. I know the feature exists but you have to manually set it up. Your phone is encrypted by default. This is an extra layer that prevents Android from booting untill set password has been put in. You can try your unlock code/password/pattern.
Yes it can. I replaced the screen of an iPhone 7 with a faulty digitizer. The top half worked fine, but the bottom half didn’t work at all. Simply replacing the screen fixed it. It cannot be the lcd. The lcd simply displays visual information. The digitizer is the thin piece of glass that registers analog signals (touch, swipe etc.) and converts it to digital signals which it then sends to the device. A digitizer and lcd are two different things.
Remove the battery, hold power button for 30 seconds and plug it back in. Here is a link to a guide on how to remove the LCD screen, also covers how you can remove the battery. BLU Vivo XL2 LCD Screen Replacement
What is Marshmellow custom ROM? Custom ROMS tend to have these problems. I recently flashed my old OnePlus 2 to LineageOS and installed OpenGAPPS. The Play services are constantly stopping. It has worked in the past. Try to flash it again and install opengapps.
Might be your HDD dying. (1) Try resetting the BIOS to default settings and see if that works. (2) Get a Windows 10 installation usb stick and run startup repair (3) Install Windows on a fresh HDD and see if it boots from it
Try the following. (1) Remove the battery and press the power button for 30 seconds (2) With the battery removed, plug in the charging cable and check if you can boot If that doesn’t work, your battery is dead.