IP checking might be a good idea nonetheless, and take the risk of losing those users with identical IPs.
Or, you could use cookies which will be stored on individual machines.
How about a three pronged approach?
1) Check Email Address
2) Check Cookies
3) Check IP
If their IP exists in your database, but their email address doesn't and they don't have a cookie, then your chances are probably very good that it's a unique user on a LAN, so you can process their submission.