This sounds like a hardware problem. I know this seems basic, but when you move, do you see your updated current position on the map? Do you see your current position in another GPS program, such as Google Maps?
If no better idea is forthcoming, you might take a look at Plugins > Trip recording > Settings, though I'm not sure if any of these would prevent the track from being recorded.
Hi Majka- In the Fairphone OS > Places > OsmAnd+ > authorizations: I give all rights (Cam, Micro, Memory, Places)--> no improvement