With all due respect, you used a weak password and don't remember what email address you used to sign up to Skype? If Skype was of any importance to you then surely you'd know what you email you registered with at the very least.
I have found in general, FREE Microsoft support to be very poor. I have needed it in a few occasions (Azure VM broken by an Azure update, XBL email change, and a few others) and each time it was a very painful process. Contrast with paid support - my experience is through the dev channel - it is amazing the access to resources you can get.
Microsoft really need to do something at the free level. I won't hold my breath, but every time I need to do something with them I prey the solution is simple. Sadly, oftentimes it is not.
I've heard of others having this problem with Skype before, so after reading your story, I investigated how to find this information. The process in this link definitely results in a date that is in the right general ballpark. I haven't had cause to authenticate my ID with this date however.
Because this method exists, verifying by incept date is kind of stupid on MS's part. A hacker would also, if he's got control over your account and has you logged in on his device, be able to perform this procedures.
