From the Keyclone FAQ
can i move it to another machine yes. your license allows you to move your activation to whatever machine you wish... but that process is a manual one, and requires interaction on my part (in other words, it could take a day or 2). contact me with your old system id, new system id, and your email address you used with paypal. once i have those, i will invalidate your old license and activate your new one. (i really should make a webpage for this...)
Basically the serial code isn't what is needed it's the system id. =/ If you still have your paypal receipt then it should have the system ID on that.