El capitan upgrade takes forever (>48 hours) Problem

I am currently updating a computer at work to El Capitan. After downloading, I started the installation almost 48 hours ago and it hasn't finished yet. I know (by experience and through reading various threads) that El Capitan is pretty slow to be upgraded but 48 feels dangerously too slow.

Machine

Note that the machine has 500GB of storage and has been used in the past mostly for storing things and for running various processes coded in C, C++ and R.

How it looks like

The screen is blue and empty with only the below loading sign at one third of the height from the bottom. I did not stare at this computer for the past 48 hours of course, but I would tend to think that it reached this screen in a matter of minutes and then jsut got stuck there for the past 48 hours.
The chance that something useful is happening is low. If you are comfortable with terminal or have a second Mac I would power off the Mac and then examine the /var/log/install.log and /var/log/system.log to see what has transpired to get stuck.

Restarting the upgrade or reinstalling the OS from Recovery HD should be harmless and would very likely succeed.

You could also power off the Mac and connect it to another in Target Disk Mode and get a backup if you have none / don't trust the backup / it's not current. That way you can erase and install and migrate your user, settings and apps back using Migration Assistant or do it by hand.

Unless you can ssh in or use remote desktop to get the files mentioned above, you have few options but to pull the plug and pick up the pieces.