Since you already replaced your computer with your iPad, and if you do not have access to your old computer, you have two options to recover the your friend's email addresses.
First, this will only work if you were using a web browserlike Internet Explorer or Safari to send and receive your emails. This is because all your emails and contacts are saved in the web server and NOT in your old computer. To try this option, please use a web browser and access your email there and see if all your emails and contacts are intact there.
If you are using Gmail, go to http://gmail.com. If you are using Hotmail, go to http://hotmail.com. If you are using another email provider, please tell me so that I can give you the webmail link for that email provider.
If you were NOT using a web browser to send and receive emails in the old computer, then it means that you were using an email program like MS Outlook or Mail. In that case, all your emails and contacts were saved on the old computer.
In this case, your only option to get your friend's email is to contact her using other options like mobile phone text/call. However, if emails was your only means to communicate with her, your last option is to perform a reverse email search. This is done using a reverse search engines available online. But please note that most reverse search engine providers require you to pay to view the search results so this can be your last option.
The only free reverse people search engines are the links I listed below. However, not all of them list the email address as they are always confidential. But they list phone numbers so you can contact her directly and ask for her email:
Pipl Search => https://pipl.com/
In that page, just enter the name of your friend. To narrow down your search, you can enter her address as well.
Whitepages => http://www.whitepages.com/person
The last search option is the paid one, known as the Spokeo People search. They are the leading search engines for people and reverse search. Here is the link:
I hope that helped.
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