Auto focus not working, I suspect dust behind the lens

If you can get clear images focussing manually then I doubt that dust is the problem.

If the camera has been heavily used (many thousands of images) then this could be the same problem as the first camera I fixed.

The focusing lens is the last component before the image sensor and is moved forwards or backwards by a motorised leadscrew which engages with a threaded brass insert in the lens carrier. This link shows it, albeit for a different camera, though it’s likely to be similar. Eventually, the thread in the brass insert wears out and no longer moves the lens reliably. You can get a replacement brass insert by cannibalising another camera with a different fault - faulty cameras are available cheaply on eBay.