There are currently no logon servers available to service the logon request

Solution 1:

Your wording suggests that perhaps those users have never logged on to those laptops while the laptops were connected to the network. In such a case their credentials have not yet been cached. The laptops must be able to communicate with the domain controller for at least one login per account.

Solution 2:

Windows 7 is booting too fast on new computers. Windows get's to the logon screen before the network binding process is finished. In addition to Leo's advice: "If the issue persists, you can check “Always wait for the network at computer startup and logon” policy is disable under Computer Configuration/Administrative Templates/System/Logon in the Group Policy." http://techdom.nl/microsoft/disabling-domain-logon-wait-time-when-no-domain-controller-available/ Computer Configuration > Administrative Templates > System > User Profiles > Set Maximum wait time for the network if a user has a roaming user profile or remote home directory.