If you're not going to replace the hard drive you need to make a LiveCD type bootable drive and not an installation drive.
Here is an example of a bootable LiveCD:
Ubuntu Desktop: http://www.ubuntu.com/download/ubuntu/download
It's a complete OS on a flash drive that doesn't need a HDD to run.
There are some guides to making a Windows version of a LiveCD but it's not a complete OS like Ubuntu. It's more of a RescueCD to help gain access to a HDD (which you don't have).