I have another popular cheap dash-cam from china which had the exact same problem as the original post, getting stuck on the startup picture with no switches working except the 'Reset' button which switched it off.
I tried most of the things suggested in the posts above including fully charging it, trying different cards and flattening the battery as far as you can but without any success.
This particular camera has a built in LiPo battery which cannot normally be changed by the user so I couldn't try swapping the battery.
Realising I probably wouldn't get much help from the supplier I took the camera apart myself and desoldered one wire from the battery and then re-soldered it back on.
This did the trick and the camera is now working normally so whatever causes this problem seems to be cured by a complete reset.
I hope this helps others with the same problem, although I realise some people might not be comfortable with or competent enough to take a camera like this to pieces and put it back together again without damaging it.
Don Stewart.
P.S. Now I have the camera working there are other major problems with the video resolution, it looks as though all the modes are interpolated up to whatever resolution is selected from the menus from a very low number of pixels in the imaging chip itself.
The results look even lower resolution than the 640 x 480 lowest selectable mode, I would guess the chip is actually a quarter VGA 320 x 240 or slightly better.
Number plates cannot be read and even the details of peoples faces are so blurry the recordings would be useless in an accident.
There is no way this is a Full HD or even 720p camera and I will have to decide whether it's worth arguing with the supplier about this to try to get a refund, since because I had to take it apart to get it working I suspect they will not honour the guarantee.
I have attached an image from the eBay page of this camera, to help anyone thinking of buying one of these,
I hope this is not against the rules.