No there are no "liveCD" versions of Windows that work (like full versions) - the licensing terms and checking systems of Windows, especially since XP, tie the OS to the hardware it runs upon. So a "liveCD" that you could boot up on any PC like a Linux LiveCD does, would either be poorly configured with the hardware - like the UBCD for windows which has pretty fuzzy graphics, and is pretty slow in operation.
What Linux can do and Windows can't is build a small kernel for your hardware and run it in an area of your RAM, as if it were a hard disk. Windows comes nearest to this with Windows PE and RE (The preinstallation and recovery environments), the greatly cut down versions of Vista/Windows7 that allow installation, startup and recovery repair when booted up from CD/DVD, but the few programs capable of running on PE or RE are things like Notepad, the Command Prompt, Regedit and TaskManager. You get basic networking, but not enough functionality to run a browser like you can in a live Linux.
Without a hard disk, you may find it difficult to burn a DVD - there is no virtual memory to cache all that data to, so all the source data will have to reside in memory - alongside your live Linux system - you will probably end up spoiling the blank DVDRs.
I'd do the sensible thing and replace your hard drive.