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.
Definitely try to get the recovery disc from Apple first. It will be less expensive.
If you're sucessful you will not need to buy the full retail version.
Remember to determine the G5's serial number first: