It’s largely going to depend on what version of Windows you are coming from on the old computer and going to on the new computer along with what e-mail client you are coming from and going to.
If you can provide some information about your setup, I’d be more than happy to assist you.
Since both computers are Windows 7, with our Windows Transfer Cable, using the built in Microsoft Easy Transfer Wizard in Windows 7, it should be able to transfer your Windows Live Mail email contents and settings.
It may work best if the old computer is upgraded to the same version of Windows Live Mail the new computer is running, but it’s not required.