Hi there and welcome
Can you remove the battery please then hold the shutter button down for 60 seconds then release.
Wait 5 minutes, put the battery back in and try to turn it on.
Tell me please if it now starts correctly
Can you power it off please, turn it upside down and put it on something that vibrates such as an electric razor
Then turn it on and off 5 times and tell me please if this gets the lens to come out and allows the camera to function.
It is the internal drive motor or the gearing that has faulted. All other causes have been ruled out
I am really sorry about this and you are going to have to return the camera to have this replaced. It will be covered by the warranty if this has not expired, and the replacement will be done at no cost to you.
I am really sorry about this, and if you have problems, or would like any additional information or assistance, please do not hesitate to let me know.
And if you can take a second to rate my service by clicking one of the stars at the top of the page, then submit, that would be greatly appreciated.