Strictly speaking no you can not transfer the operating system to your new PC as it would have more than likely to be what is called an OEM version ( original equipment manufacturer) which means in effect that it is tied to your original PC and cannot be moved to your new one.
Then you have the problem of the drivers for motherboard etc these will be different as you new PC will have a different motherboard so a new installation is really the best way to go.
Your program's will also need to be reinstalled but this will make it a little easier.Ninite. this will enable you to install multiple popular program's at the same time.
You could take this opportunity to upgrade to Windows 7 which will cost you around £70 of buy a retail copy of Vista which is around £55.
It is certainly a good idea to back up your personal files to your external drive but you can also slave the hard-drive from your old PC to your new PC,once you have an operating system,and copy the files that way.