I cannot turn on the System Configuration in Advanced option of Text Services and Input languages.
When I turn off this option, and apply it, then I close it and get back. That System configuration status is still turned off.
In the Group Policy Editor browse to User Configuration -> Administrative template -> Windows components -> Internet Explorer -> Disable change language settings. You can enable the policy from there (This either allows or disables a user's ability to turn on/off the service)
If you are a programmer you could try using OllyDbg (download here) to see what happens when the options get saved.
If you are an expert user than you could try using Process Monitor (download here) to see if it has changed a setting in the Windows Registry.