I have an imac with OS X and can access https sites just fine in the administrator account. The other account cannot access https sites - using safari or firefox...
I have repaired the keychain (first aid), and later removed it - to no avail.
I confirmed the firewall security settings allow all incoming connections.
I have parental controls activated for the non-administrator account, but also have them setup on another imac which works just fine for both the admin and user. They seem to be setup the same.