Profiles list not showing in dropdown list in Online Registration tab of Configure Event
After more investigation, the problem is solved using the fix from agh1 (thanks to him by the way).

It looks like a problem in the civicrm code using jquery.

Here is the url of the fix. We tested it and it works. 

https://github.com/civicrm/civicrm-core/pull/10152

I hope this will be in the next civicrm release code.