Yes it's technically possible if I follow these steps:
Step 1. Pay $2400 to a hard drive recovery company to retrieve my data.
Step 2. Look at my skype password.
Seriously, I did try password recovery but couldn't because I no longer have access to the email address which I used to sign up to Skype, and the reason I don't have access to that particular email address any more is because... my hard drive failed.
I back up a lot of stuff (95% of it usually), but got caught out this time by the last 5% that wasn't.
I'm thinking that this person I'm looking for might have been 'error'... I'll PM him