The official website doesn't work anymore which means you will have to manually transfer the software on the new computer. You can use a USB flash drive and copy the contents of the installation directory. However, you will need a serial number, but because the official website is discontinued, it's impossible to obtain one. If it doesn't require online activation, I believe you can use the old serial number to register it.
I recommend choosing a free application that gives you the same functions as the one above. It's called Audacity and it can be downloaded from the official website.
