I had this same problem Was getting hung up before shutting down on the cleared desktop image (which happens to be a grey screen for me).
I talked to Apple support who could not figure it out, and recommended that I go to the genius bar, which would have been really time consuming. I figured it out by turning off any apps I could that were running in the top bar, and narrowing it down to one offending app - an app used for beaming my screen to iPads and monitors called "air display host" had something to do with it. Avatron the makers of Air Display host should have published that they were causing a bug in El Capitan.
Apple should not push this upgrade at us so frequently if it causes conflicts with so many common popular apps likes the ones mentioned in the forum which are sold in the app store. Doesn't apple have a way of checking with their app developers to confirm that their software works with the beta version of the OS and is not about to crash it completely? If apple has some oversight on the products then they need to own up to that and somehow communicate that some apps will not migrate over, and will actually mess up the whole system. How is there a total gap in communication between Apple, developers, and the custome? When apple is claiming oversight over the contents of the app store, how are there apps that migrate over and then totally mess up the OS, without any customers even being notified, and without any way for Apple support to diagnose the problem? Isn't that the whole point of such a self contained store with apps that have all gotten a stamp of approval? I could understand if this was an app purchased outside the app store causing the problem, but there's clearly a gap here that needs to be addressed.
I'm just taking the computer back to Yosemite using a time machine backup. Good thing I had a weekend, this process is very time consuming. This is the first time that I've not been able to update to a new Mac OS just because the migration is so glitchy. Even without this hangup, I was also getting a 25 seconds mysterious black screen directly after login. I'm not sure if thats part of the new startup sequence, but it's really disconcerting to see a long black screen immediately after I login. I love apple, and thank goodness for time machine, but sorry El Capitan, this is too bumpy of a start.