To boot your existing Windows 7 HD on new hardware, first SysPrep on the old hardware to remove all drivers
, SID's, HID's and activation. Then it will start up like a new install but with all of your programs, files and settings maintained: SysPrep to move HD to another computer
If you don't have access still to the old hardware, then boot Paragon Adaptive Restore CD on the new hardware and point it at the Windows 7 installation. It will do the same things as SYsprep so the new install will start.
Only in rare cases will Windows 7 start on new hardware, so there isn't any way to say for sure except don't count on it.
A clean reinstall is always a good option and actually better than getting a new computer since they are all larded with factory bloatware and useless utilities with better versions built into Windows 7. Here's how to get a perfect reinstall of Windows 7: Reinstalling Windows 7