You can certainly buy a new hard disk drive and install it. OWC / MacSales is a recommended vendor.
You cannot download an OS from Apple on that machine. You would need to buy a retail package of OS X on a DVD. You can install up to Leopard; not Snow Leopard.
Strictly speaking, a used Mac should always be sold with its original system installation discs. They are supposed to be included with the hardware according to Apple's licensing agreement. I would not consider buying a used Mac without them.
It cannot boot since there is no device from which to boot.
Retail versions of OS X tend to have insane prices, so shop around.
You could try to obtain replacement system installation DVDs for that computer by contacting Apple, but I do not know if they have them or what it might cost. Have your system's serial number available, they won't be able to help at all without it.