Firstly, in copying over the entire contents of the old hard drive would copy over the old operating system. This would not work as the old OS would not have been set-up for the new PC.
Secondly, virtually all of your old software will have been "installed" on the old PC. "Installation" of software entails a lot more than just copying across the program files.
You will need to source all of the software (and possibly licence keys) that you want on the new PC and install from scratch. Ninite might be a good starting point.
However, I guess you will want to copy YOUR data off the old system. You can either do this by using transfer utilities or by taking the old disk out of the old PC and putting into a USB caddy so that you can access the old disk on the new PC.