You might try getting the old tables out of a backup of your previous sites database depending on if you made that or if your hosting company has done it for you.
You can recover the table "Users" and add replace the one in your new database to add the users to your new enviroment.

If you want permissions and everything as well you need to get all tabels which start with Users

Ofcourse before attempting it I advise you to make a backup of your database incase something goes wrong.