I seem to have lost my W7 box and CD. Is it possible, with an external hard drive, to transfer the OS and licence to a new computer? Or is that ridiculous?

Take hard-drive.. Place in new pc?

IF it is a retail copy of Windows 7, then you can recover the key and download a Windows 7 ISO from Microsoft's digital store.

If it's a copy of Windows from the likes of Dell/HP/Acer/etc then you cannot.