Given the information you have given me, I would say it shouldn't effect performance, as long as you mind how you handle the screen when opening and closing. If I am seeing it correctly, then a little double-sided tape might be a better bet, but I am not sure that I am seeing it correctly. In my experience, as long as it isn't separating near the hinges at the bottom, it's not normally too big a deal. Taking care when opening and closing the laptop can extend the life quite a bit. hope this gives you an idea what to expect, sorry I couldn't help more.
It sounds like you need to create or buy an installation media. The link I am providing will allow you to create a USB install drive from another computer. Once that is created it will allow you to install Windows 10. Although, because this is a new build, you may not be able to use the key you had from the previous computer. Windows 10 will still work, but it will tell you that it is not genuine until you either buy a new activation key, or sometimes you can contact them and they'll allow you to reactivate the key from the previous computer. (Sometimes) Also, installing Windows will wipe whatever is on that drive, so please make sure you install in on the intended blank drive. https://support.microsoft.com/en-us/help/15088/windows-10-create-installation-media
Do you have access to a windows 8, 8.1, or 10 install usb/disk? I have booted from those before, then used the repair option on the second screen. A startup repair from there might work. You might need to acquire an external optical drive for a disk, of course. Have you tried also using program in command prompt? Sfc perhaps? I have found that normally the issue you're experiencing is related to explorer.exe not working correctly.
In my personal experience, system updates or malware are commonly the culprits. I would suggest to run an AV/malware scan. If that doesn't fix the issue.(make sure to reboot before testing) Either goto a previous restore point or refresh your system, depending on your OS. Once you post your OS, I can tell you how.
It sounds like it is a damaged connection of some sort. If the the screen was the problem, you would have dead pixels or visible cracks in the image. Look at the hinges of the device, often if they are damaged then that is where your locate the issue I haven't had the best luck in working on this kinda problem, but anything is repairable if you want to put the effort into it. Have you tried connecting to an outside display? Then you rule out a software glitch.
In my experience, you are probably right. It is probably you hard drive malfunctioning. It depends how far gone your drive is, in regards to how easy it will be to recover the data. In many cases, removing the hard drive and connecting to another computer as an external drive will allow access to the drive. You can get an USB to IDE/SATA cable for around $20 from Newegg. They are easy to use, and, if the drive is still somewhat functional, it will be like taking information off a thumb drive. If the drive is too far gone, you may need to pay a professional, but normally the cables do the trick. You will probably need a new hard drive & operating system, if you want to continue using the computer.
There is a good chance that something negative has happened to your hard drive. I would suggest going into your bios first. (When you first boot the system, hit the button that will give you access, normally ESC, DEL, or an F key) See if you can locate your hard drive (it may be referred to as HHD). If it lists the HHD, then you are probably experiencing software issues. If it is not listed, it is more likely a hardware issue. I can post additional help after you get to this point, in the comments.