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.
Best Answer
Apple Support: 1-800-275-2273 (Or you can get it from here)
Call, it wont take long, and you don't need to have applecare or anything like that. And this way, if something breaks, maybe you'll be eligible for some kind of reimbursement.
You can do the whole thing with your phone on speaker. I actually tried to call them myself (and then relay the information) but one of the first things they ask for is a serial number.
The occasions i've called them are all blurred together, but i vaguely remember being told to hold the power button for some specific length of time, holding some key while it started up (which might have been to activate disk utility), and unplugging the iMac.
The key thing, though, is that i called them, it didn't take long, and in doing so i was able to fix it.