No, you can't run Windows that's on the old hard drive on your new PC, totally different hardware will cause a whole bucket-load of problems, plus it's illegal to use a factory pre-installed OS on a different computer.
You can install the old hard drive as a storage drive on your new PC but you will have to install your applications & games from scratch using the installation media or setup packages that you used to install them before. This is because the Windows installed on your new PC knows nothing about those apps & games, there are no keys or entries related to them in the registry, no support files in the Windows folder, and no program folders related to them.