Why do computers not work without a harddrive?

Computers work just fine without a hard drive, but they don't do much. In companies it is common to have computers that get all their files from the company network. No hard drive. If you go to a hotel there is a computer in every door knob that reads your key card and decides whether to let you in. No hard drive. In fact, computers were invented before hard drives. The first disc drive was announced by IBM in 1973. Development was a secret, and disc drives were called "Winchester" for a long time because that was the code name for the project.

FYI a drive is anything that transfers a fixed amount of data with each access. Drives might be hard disc, floppy disc, tape, solid state, or anything else, as long as they transfer a block of data at a time.