https sites don't work for users

[iamtooshy]

The problem is easy to describe:

If a user goes to a https site, IE loses connection. If Administrator goes
to a https site, it works fine.

I know one thing: No firewall issue, it's a certficate thing. If I go as a
user to Internet options->content->certificates and try to view some of them,
I am getting the failure, that trust couldn't be confirmed.

I can view them without failure as Administrator.

It happens on all clients on the domain.