FBW - as I said, what you want to do isn't impossible, just an order of magnitude more difficult than the standard answer that most of us have suggested.
You'll need to create a boot floppy that gives you access to the network. These are used in diskless workstations and by system installers. I've never done this so I can't give you any specific instruction. Mobos, network cards, protocols and network access are all pretty individual so the bootdisk has to be a bit tailored to your installation.
I searched Google for boot+network+windows and got you a couple of starting points.
Have a look at
http://www.appdeploy.com/faq/browse....otdiskcreation which should give you some ideas. Also
http://www.i386.com/default.asp?c=6&k=12 et. seq. and
http://www.pctip.ch/downloads/dl/22842.asp
This looks promising: "Bart's msclient bootdisk
http://www.nu2.nu/bootdisk/network is a customized TCP/IP network bootdisk that enables you to connect to a network share on a Windows NT/2K or Windows 9x/ME machine using a range of network cards." - seems as near to a generic bootdisk is you're going to get.
I think you should be prepared for a bit of hacking and relevant forum browsing. Unless you're very lucky first go, by the time you succeeded you'll know more about the esoterica of floppy and remote network boots than any of us, so _please_ keep us informed.
[Another alternative, if your mobo BIOS supports it, is PXE boot from Network. I don't know much about PXE boots, so you'll have to research it yourself. There are even PXE-on-disk utilities available (try
http://www.argontechnology.com/mbadisk/index.shtml ) but pricey and I have no idea of the details of how they work.]
Once you've gotten C2 connected to C1 _without_ the aid of the original HDD but _with_ access to it, you can dump the contents of that drive onto C1 using xxcopy. You can then install the new HDD onto C2, fdisk it, make the boot partition active, format it, reconnect to the network with your boot floppy and xxcopy the copy of the original HDD back to the boot partition of the new HDD on C2. With a bit of luck it'll boot cleanly and you're away.
I think this is actually the answer that you were looking for, but it really would have helped if you had started off by explaining just why doing this fairly routine task the easy/usual way wasn't appropriate for your situation and not SHOUTING.
Edited to add: Curiosity has got the better of me (as usual) - I'm now buidling a Bart's msclient bootdisk for my own system - it isn't a trivial task. Interesting. The instructions are a bit terse but I should be able to work it out eventually.