Are there any instructions for replacing the LCD screen on a Toshiba Mini Notebook NB505-N500BL?

RTM yet, read the manual
or ask Toshiba this,
I guess you mean reset the unstated, OS back to day one new as toshiba had it?
right. the manual tells you to make recovery disk.
and my guess you never did day 1 new. that it?
if yes, then you get to buy windows again.
8 year old PC so says the the manual.
so is not w8 nor w10 there,
it seems W7, right?
so buy W7 and install it.
or try w10 for free for 30 days, see if it runs,w10 does not like PCs too old.

page 50 shows " how to recover to the out of the box experience"
day1, all your data gone, all your apps gone. RTM or ask at toshiba forum we are not toshiba at all, not even close.... ok?

https://www.manualslib.com/manual/203382/Toshiba-Nb505-N500bl.html?page=20&term=recovery&selected=1

sounds like a loose lead connecting up the screen, if you take it apart, look for a flat strip with metal lines on it going into a socket in the top half, from the bottom half.

1. Get an RGB cable.
2. Plug one end of the cable to the laptop VGA/RGB port.
3. Plug the other end of the cable to the RGB/PC input port of the TV.
4. Select the output of the laptop to the VGA/RGB port.
5. Press the Video button (usually with a sign of an arrow inside a circle) and choose PC.

Somehow, the HDD password has been set. Unless you can remember it, you MAY need to replace the HDD to get around this. I have 'bricked' an HDD in the past in this way.

There is a company on the Web that, for a fee, will help you break that password. The fee depends on the size of the drive. However, to get access again, the HDD will have to removed and reinstalled into an empty SATA/IDE port on a 32-bit desktop so their online server can remove the password. Might be easier just replacing the drive...

Hard drive failed, replace it

You can download a service manual from this WEB site.
http://www.pdfuu.com/toshiba-mini-nb505-manual-users-guide-troubleshooting.html

You can do this from the Bios itself. Depending on your system press either F2 or DEL during start up before the windows logo is displayed. Go to security and you can change the password there. You will have to have the current password in order to do this.

Windows files has been corrupted, or the hard drive has issues. This is where a backup recovery disc would be ideal, this would prove hardware issues. At this point have the hard drive tested for errors and bad sectors to see if replacement is required.

Laptop hinges cannot be tighten, there are no adjustments available.
The hinges need to be replaced.
Replacing a hinge, or both of them, isn't very tough this WEB site shows how it is done.
http://www.insidemylaptop.com/replace-br...

Your motherboard or battery may have died. Have to repairman check it for this.