There are two reasons this will be difficult, assuming your computers are running Windows 2000 or XP:
- The new computer must have identical or very, very similar hardware (same system board chipset)
- Windows activation will require reactivation on the new system, which you will need to call up MS and explain the situation to them.
Is it possible, but will require some effort on your part. Once you transfer your old drive (or clone the data) to the new computer, try it. There's a 95% likelyhood it won't, but it is worth a shot. Once it fails, you can perform a system repair.
The details are here. Please realize that you will need an original Windows 2000/XP CD that matches the version of Windows installed on your computer (eg. Windows XP Home OEM is different than Windows XP Home Upgrade as well as different than Home Retail and of course different than XP Pro etc...). Some manufacturer discs will not work because the use a customer installer (Sony, to name one) which do not allow the repair process to be done. Chances are, you will need a Windows XP Home OEM or Pro OEM disc, if you're using the original installation of Windows from the manufacturer.
So, with all that mess out of the way, you'll basically be reinstalling Windows 2000/XP over itself, but it will retain your settings and the majority of your configuration. Once you manage to get the system to boot, you'll need to call the MS activation hotline and activate your Windows. Tell them you've upgraded your system and only one copy is in use (do so only if the old computers are getting thrown in the trash or will be using different OS software).
All in all, it doesn't sound like what you want exactly, but it is the only way to get it done... done well, that is.
Even this is not 100% though, as there's also going to be some issues. You'll probably need to reinstall Office and other suites that integrate into Windows because they'll no longer run properly... You'll need to run Windows Update your computers again because all Windows Updates will be lost etc.. But your data will be there. Some system settings can be 'reset', as such I've had network adapters with customized network setups reset and so on.