To what extent can a computer be reset to factory settings?

If you want to "reset" a computer as near "pre-assembly specs" as possible, you need to wipe the drives, reset the BIOS and disassemble the individual parts.

Wiping the drives, so that they are completely empty or filled with random bits can be achieved with a bootable (USB/CD-ROM) system like DBAN: https://dban.org/ (instructions to create media, etc can be found under Help / Installation Questions).

If your computer(s) are already disassembled, you need to connect the drives to another computer (via USB or internally via SATA) and do the wiping there.

Some BIOSes offer a disk wipe option (mostly laptops, though), so it might be worth checking that out too.

BIOS (or UEFI, whichever you have in the computer) settings can be reset in the BIOS itself.

It is possible to boot a computer without installing the OS on the hard disk. This is what happens with DBAN. The DVD or USB contains an image file of an operating system which is loaded into memory, making the computer function. On DBAN, a program is loaded which writes to a hard disk, removing and obliterating all the data it contains. When the computer is switched off, the OS disappears from memory, leaving the disks blank.

Some information is held in nonvolatile memory on the system board in the form of BIOS settings. These are often maintained by a battery which can be removed.

The entirety of the OS depends on the first few sectors of the hard drive. Without this critical first sector, the entire hard drive may as well be filled with random bits. You can grab a Live Linux OS disc, pop it in to your computer, and run a command like the following (run as root):

dd if=/dev/zero of=/dev/sda bs=4096 count=4096

At this point, the GPT or UEFI structures at the beginning of the drive will be zeroed out, and the computer will not be able boot at all, as if the hard drive were brand new (though there will be bits and pieces of the OS scattered throughout the rest of the drive).

It's important to note that the OS is not installed on the computer, it's installed on the hard drive. You can move the hard drive from one computer to another and the OS may run on the new hardware. Note that using the command above will render the drive unusable in any computer until it is formatted.

NOTE: Make sure you check the location of the hard drive before using the command. Not all Linux systems will map the hard drive to /dev/sda. You can use the lsblk command to verify the device that the hard drive is mapped to. (Thanks to @HSchmale for the comment).