If you've done nothing else to the El Capitan, to start in Safe
mode could help; at least to get past that restart issue..
How to use safe mode on your Mac - Apple Support
//support.apple.com/en-us/HT201262
Extra links in the above could help to install/reinstall an
other macOS version, help find & use recovery versions
among other small details that could make or break this.
Once you've upgraded to El Capitan, an idea which may
work better, might be to try for High Sierra 10.13.6; as
that might give the hardware a patch for firmware; but
you may just erase and install a higher macOS instead.
Mojave 10.14.6 is a fairly good one; and link to get download
is from the same page others were located. Be sure to get
installer downloads with Safari browser; instructions indicate.
My Late 2012 Mac mini quad-core server, has two rotational
hard disk drives; those are a known bottleneck too. At least
one of them should be upgraded to solid state drive. Present
those have two partitions, in each as well. (Has four macOS.)
(You could consider starting up from Internet Recovery; and
then use the internal recovery to erase the El Capitan. If you
like; from the Recovery partition; start with Option Key held.
..And be sure to 'back track, on exiting' each item used there.
Sometimes this works well; other times, not so much.)
I'm a bit rusty on these things; have to admit. Had given
older Macs away; in working order. Still have G4 Mac mini
Late 2005 w/ 10.5.8 (& tenfourfox last stable version).. And
mid 2012 MacBook Pro 2.5GHz core-duo with Mojave, on
a smaller 240GB SSD (third party, has Flash, no HDD.)
So I have done some maintenance, boot from Internet Recovery
and occasionally run that version Disk Utility to check & repair
drives, etc. With later MacOS, these new Systems create more
nested internal partitions; and these have their own rules, too!
Perhaps you may choose to ask a new question, as a 'marked as
solved question' may deter others from reading your newest one.
This could help get additional attention; also look into Mac OS
systems communities, once you choose ideal macOS version
as final destination; those areas have upgrade topics, beyond
that are inclusive of hardware limitations. (HW limits upgrade.)
Some active newer users have a dogpile of evidence of their
credible worth. Whereas my participation has been less active
from an initial start, in 05/2003; the original 'Apple Discussions'
is long gone; several topic histories have vaporized too.
..To say my offline life is rather overwhelmed in the
present time, would be an understatement, as well.
