You can't get info about the client computer easily - it is possible, but it opens up security holes which it's difficult to plug up afterwise.
A better approach would be to send an email to each authorised user which contains a "click here" link to a "hardware validation" page on your site. If the link contains a query string which you check in your DB (a different Guid per user is good) and if it is correct and not used yet, writes an authorisation cookie to the client computer. You then check the cookie in your "normal" website and if ok, show the login screen or just treat them as logged in.
Sounds complex - but it isn't. The email link is just a standard HTML HREF with a query string:
<a href="http://MyDomain.com/validation.html?id=9dcb491f-0edc-46d7-bc5a-6994416179a7">Click here to validate</a>
In the page, all you have to do is read the query, check it against your DB and write a cookie. Simples!