What are the differences between hardware and software?

Computer hardware is any physical device used in or with your machine, whereas software is a collection of code installed onto your computer's hard drive. For example, the computer monitor you are using to read this text and the mouse you are using to navigate this web page is computer hardware. The Internet browser that allowed you to visit this page and the operating system that the browser is running on is considered software.

All software utilizes at least one hardware device to operate. For example, a video game, which is software, uses the computer processor (CPU), memory (RAM), hard drive, and video card to run. Word processing software uses the computer processor, memory, and hard drive to create and save documents.
In a computer, hardware is what makes a computer work. A CPU processes information and that information can be stored in RAM or on a hard drive. A sound card can provide sound to speakers and a video card can provide an image to a monitor. All of this is hardware.
On that same computer, software can be installed and allow a person to interact with the hardware. An operating system, like Windows or Mac OS, is software. It provides a graphical interface for people to use the computer and other software on the computer. A person can create documents and pictures using software.

Can a computer run without software?

In most situations, yes, a computer can run without software being installed. However, if an operating system or interpreter is not found on the computer, it either generates an error or doesn't output any information. Installing programs onto the computer in addition to an operating system gives the computer additional capabilities. For example, a word processor is not required, but it allows you to create documents and letters.

Can a computer run without hardware?

This depends on the hardware. Most computers require at least a display, hard drive, keyboard, memory, motherboard, processor, power supply, and video card to function properly. If any of these devices are missing or malfunctioning, an error is encountered, or the computer will not start. Adding hardware such as a disc drive (e.g. CD-ROM or DVD), modem, mouse, network card, printer, sound card, or speakers are not required, but give the computer additional functionality.