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You'll need a retail Win7 license for the Win7 version, whether you use the old install or Clean Reinstall - Factory OEM Windows 7.
If you want to try starting the old Win7 HD or image to see if it will start, first go into BIOS setup to disable Secure Boot, and unless you had UEFI on the old laptop (doubtful) enable Legacy BIOS, or if there is a Compatibility Support Module choose Dual or Legacy choice - providing that's what your old Win7 was installed as.
Now see if it starts. If so it will swap out a bunch of drivers requiring several restarts so monitor that closely. You 'll need to change to a retail Activation key at Computer>Properties.
If it won't start and you're sure it's a Legacy BIOS install with the current BIOS set to that, you can either Clean Reinstall or try adjusting the OS to boot on the new hardware with Paragon Adaptive Restore CD freeware.