You'll just have to sysprep the HDD before plugging it to new PC to avoid boot BSODs. To do this, go to C:\Windows\System32\Sysprep\sysprep.exe, check 'generalize', select 'OOBE' on drop down menu, and 'Shut down'.
When your new PC boots off of your old HDD, you'll get the 'out of box experience' screen, asking you to create new user account. Just call it anything and after that's done, you can log off and switch to your main user account.
Once you're logged in with your main account, you can safely proceed with deleting the newly made account in Control Panel > User Accounts applet
To clarify what sysprep does, it basicly gets rid of all platform specific data such as drivers and configuration files.
Otherwise you will have to do a clean install of windows, etc.