For only a few users, on login, SharePoint 2010 returns blank page

I have never experienced it myself, but I've seen a post where somebody told that in his case the cause was the fact that failing users were on a different branch of AD. I am not sure that his case was about blank page, but probably it is cause of your case too.

I don't know whether it could help, but I would try to check User Profile Synchronization settings and do Full User Profile Synchronization.

Hope it helps.

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Regards Michael (http://sp2013-blog.com)

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