After migrating the Farm from SharePoint 2010 site to SharePoint 2013 platform (Under Same domain) using the “Mount-SPContentDatabase” command, users were unable to login or access denied. When grant permission again you might note that now that particular user can access the site.
And you might also have note a prefix (i:0#.w|) has been added to username.
Solution: You have to convert the authentication method of the SharePoint Web Application from Classic to Claims
This is where PowerShell becomes really nifty. You can use PowerShell to get the conversion done.
$WebApp = Get-SPWebApplication “http://WebAppURL”
Convert-SPWebApplication -Identity $WebApp -To Claims –RetainPermissions -Verbose
For more details on Migrate from classic-mode to claims-based authentication in SharePoint 2013 you can refer this TechNet Article: http://technet.microsoft.com/en-us/library/gg251985.aspx
Happy SharePointing !!!