I think I have a faulty Bluetooth module in the head unit. The Bluetooth icon doesn't show anywhere, not even in settings. 

 

What's the cheapest way of replacing the head unit? 

Have you tried resetting to factory settings via the menu or a soft reset by holding the power button down until it powers on and off again? Try those first as a replacement radio is a bit of a big deal, will involve a used radio of the same type having the component protection removed and coding done to match the old radio or you can upgrade via unofficial routes but that can get expensive if you just want to fix the problem and you are happy with the radio otherwise.