have a read of this post and you'll find out how to back up your key.
but did you not back up your key to a floppy/cd as by the email slysoft send you? or save the email's, as your key is an attachment on one of them ?
Edited for ppl who can't click on links
[B]The Key for AnyDVD is stored here 'HKEY_LOCAL_MACHINE\Software\SlySoft\AnyDVD\Key'
Open Regedit browse to the above location, highlight 'key' and choose File > Export.
Copy and Save onto your desktop PC.[/B]