Thats a difficult one, also I think the insurance company when filling out the forms detailing what happened, will be wondering why your making a U-turn on a one-way street, so by doing that you will have been to them driving down the wrong way at some point.
I wonder when you say that you hit a barrier blocking the road its a dead end street not One-way?
But all that it shouldn't matter, if you had taken out insurance to start what ever time of that day, and you have paid a premium either by debit card on phone or been in in person, as long as the accident had happened after the time your insurance started, technically a claim is feasable, tho waiting a few days than making a claim, and lieing on the form about the date thats fraud.
With insurance it is ALWAYS best to be truthful, insurance companys do there best not to pay out anyway, so slightest bit of wrong info and there pick up on that.
Also you don't mention any damage to your car or barrier, just that it won't start, insurance doesn't generally cover mechanical problems, that comes under warrenty when you bought the car, tho if it down to crash damage your out of luck there.
I think you should just go to the insurance, with the details of what happened and the time it happened, and as said earlier if it happened after the insurance start time technically a claim is feasable.