You will at minimum have to do repair install of windows (will not wipe the other data) and install the drivers for all the new hardware. If it is windows7 you are running then it is very forgiving and might fix itself.
If it is windows7 it is a change it will fix itself on startup but if it does not then start from the win DVD select install and when it detects a previous installation it should give a option to repair.
at least uninstall all the system drivers for the old system before you try this. Its a bad way to do it and may affect performance and cause other hard to diagnose problems, more so since its a new system and you wont know if its the hardware or software/driver issues. Its also a violation of the license agreement if its OEM windows 7 and wont activate.
Really its not the correct way to do it and i cant recommend it. A clean install is easy and only takes a few hours so there's no reason not to do it right. And there are usually programs to read the software keys for anything you can't find.
I am fairly sure this wont work most of the time windows 7 flags major system changes now and counts that as a new system and tells you , that you need a new copy of windows I THINK that for windows now its "new mother board , new system , new windows" so ya it will boot up and probably work but they will ask for a new activation key and you will need to work that out. * as a point of example just adding a new hard drive to my system flaged me for a new key i was able to fix that but iv tried to move a main c: over to a system before and was told i needed a new windows this might not be every ones experience but it is mine.