Yes, you will likely have problems. The old OS installation has drivers and registry settings for your old hardware. You MAY be able to do a repair installation of the OS on the new system, but if you want a stable system you should perform a clean install.
Heavily recommended that you do a clean install; otherwise, Windows may complain about the hardware.
The other issue to be watching for is that hard drives are usually the first component of any computer to fail, and it contains all your data! Unless the hard drive is relatively new (eg. under 2yo) or a SSD, I'd recommend getting a new one to avoid issues later on.