FTB was running fine on my last attempt in Windows 10. Have you got both 32 and 64-bit versions of JAVA installed on your new HDD? - I seem to remember reading somewhere that FTB mod packs still only ran on 32-bit JAVA builds, so just a 64-bit pack would not work.
Also, although your CPU is 64-bit, were you runnign a 32-bit version of windows 7? - if so the upgrade to windows 10 may have upgraded most things to 64-bit, but not everything - so a fresh install of Win 10 might be advised.
Also - can you plug both HDD's in (Win 10 and Win 7), or is your system a laptop? If you can plug both in you could set up a boot loader to select which one to boot on start-up (obviously not possible on a laptop unless you have a huge partitioned HDD with a system on each partition).
EDIT: Oh - and you shouldn't have to set up an account to download JAVA - be careful as you may have gone through an unsafe website and got a dodgy download. Use
This link to download the auto-selected version of Java for you computer, or try
this page if you want a selection of versions to download