Applications think that GPS is off while it is on

I have a Prestigio Multiphone 3400 with Android 4.2.2. The phone is new and not rooted. In Settings -> Personal -> Location Access, there are two checkboxes: 1. Access to my location 2. Wi-Fi & mobile network location Both of them are checked. But the only application with working GPS is Google Maps. I tried for example GPS Test and GPS Essentials , but they both show GPS is off / GPS is currently disabled. In the Settings -> Device -> Apps -> (application name) there is "This app can access the following on your phone:" followed with "approximate location (network-based)" and "precise location (GPS and network-based)" Why are the Google Maps special? And why other apps cannot use GPS, while the permissions are obviously granted?