If you are 100% unable to retrieve your e-mail messages prior to 6-1-2016, I recommend backing up all of your files routinely (including your WLM messages) to rewritable CDs (DVD-RW), so you don't lose all of your WLM messages again.
After you make those backup CDs, I suggest you put them in a safe place, so you won't lose them and also so you'll have them in a convenient space in case you ever need to use them again for WLM and/or any other purpose.
Also, my dad has had Hotmail since 2003, since he has been a Hotmail user since that year he is "grandfathered in" to Outlook.com.
He also has to pay a small fee every three months to have extra storage on his Hotmail/Outlook account.
Additionally, my dad does genealogy, and because of that he has kept all of his genealogy-based e-mails since he became a Hotmail user back in late 2003.
Furthermore, if you [originally] had dozens of e-mails on you WLM, and if you have a similar amount now.
I suggest that you create "folders" on your WLM and put your important e-mails in those [folders] in an organized fashion.
Also, have you checked your "Spam" or "Trash" folders through your WLM?
If you haven't, I suggest you checked those two folders and see if your e-mails are in either your "Spam" or "Trash" folders on your WLM.
if none of the options I have given you help you out, then I suggest you do the tasks that the commenters above have given you.
Most young people use G-mail nowadays, Yahoo! Mail used to be #1 and now G-mail is #1 and is the most popular e-mail website.
Lastly, Android smartphones are owned by Google, and allow Android users to check their e-mail, so in a way that makes sense.