I recently tried upgrading my parents' iMac from Snow Leopard (I think) to El Capitan. It started out all right, but after the first reboot, it became very very slow. That each, each minute remaining on the progress bar took approximately 2 hours. After running for over 48 hours I had to shut the computer down (by holding the power button). Since then whether I try resuming the installation, booting the recovery partition or booting an external bootable USB of the El Capitan installation disk, I get the same thing, which is that the boot progress bar gets slower and slower, taking several hours to reach the end, and then nothing further seems to happen.
I've tried resetting the PRAN. Makes no difference.
I'm thinking this must be something in the hardware, and the next step would be to remove the hard drive and test it using a different computer.
But maybe someone out there has other suggestions?
I would add that I have a time machine backup of the computer in its last usable state, and quite happy to restore from that. But if I can't even boot a recovery partition, then I'm stuck anyway.