Lion to El Capitan upgrade stuck on restart
I had the same issue with a MacBook Pro 15'' 2011 (A1286) that I tried updating from Lion 10.7.5 to El Capitan 10.11 (Specs. 4 GB, 500 GB HDD).

The answer is: you must be very patient: the upgrade took me one full day (~ 11 hours!). 

Even if the progress bar is not updated, the update is being done in the background.

After a first attempt that I interrupted because I thought that the update was frozen, I made a second Internet recovery of Lion.
The previously downloaded installer of OS X El Capitan was kept in the Application folder after OS X Lion 10.7.5 was restored, so that I was not required to download it again. 
(The Internet recovery of Lion lasted about 4 hours).

As a comment to your picture, if you wait about half an hour, to one hour, the progress bar should move to ~20%.

The estimated times will then be completely wrong and you simply MUST WAIT and be very patient, without shutting down your computer. For instance, when under the progress bar, a remaining duration of 31 minutes is displayed, it can last about 9 hours using a wired connection! For me, things went a little quicker at the end (12 minutes meant 1 hours, 7 minutes meant half an hour).

Sometimes, the screen will show greyed / disabled, like if the computer was frozen in some manner and there might be some kind of screen flashing / flickering. Simply wait until the installation ends and the background image of El Capitan displays.

Hope this will help others.