Assuming that your "old" HDD contains a viable Win 7 OS, i.e., it's non-defective, potentially bootable, and functional, it's conceivable that you can install that disk in your new build and it will boot in that system.
Obviously there are no guarantees here but assuming that your old & new PC systems are Intel-based and these are non-OEM machines it's worth a shot. There's little (actually *nothing*) to lose.
So if by doing so you're fortunate to have a bootable, functional system as a result, you will, of course have all your programs, personal data, available without going through that rather onerous task of installing a new system.
Obviously you may have to install different drivers of one type or another in the new system but you'll have them available from your new motherboard's driver installation CD. And you may be pleasantly surprised at Windows (Microsoft's) ability to pick up & install whatever drivers are necessary for your new installation without your intervention.
Now should this all work but you still would prefer to use your "untouched" HDD as the boot drive, you can always utilize a data-migration (disk-cloning) program for the transfer of the entire contents of the "old" HDD to the "untouched" one.