Don't touch the system! Let it do its thing. You should hear a long beep tone different than you normally hear. I should point out El Capitan does do a firmware update so it will appear to shutdown and take awhile to restart. Before restarting the system I would also make sure the internal drive is set as the boot drive. The last thing here is defrag the drive using an app like this one: Drive Genius.

Next, I would delete as much as I could so the systems drive had 1/4 to 1/3 of free space. I would then boot up under an external drive and run from it Disk Utility to check & repair the drives permissions & disk structure if needed (make sure the drive is setup correctly GUID & Journaled file system).The next thing I would do is check the HD, do you have enough space on it? You may want to run this program to clear out the old cache & log files: Disk Doctor.

Follow this Apple T/N: About EFI and SMC firmware updates for Intel-based Mac computers your firmware should be at this listed level or newer.

First you should check to see what the systems firmware level is.

So lets see if we can isolate the possible issues here:

With that said I don't see why the installer would care. I doubt any one has done any testing doing an OS upgrade to El Capitan without a battery installed.

How to install os x el capitan today