Not sure this will help, but here goes anyway...
You mention pulling the batteries to "reboot" the camera.
However, in many Canon it's not just the main battery(ies) that needs to be pulled. There is also a separate date/time battery in many models. Both the main and the date/time batteries have to be pulled to get a proper "reboot" in those cameras.
5DS/5DS-R are new models, so I am not sure they have a user-replaceable date/time battery. But the two new models are based upon the 5D-series body, and those earlier models do use a one. On them it's located in a little drawer on the LH side of the camera, right below the USB and other output ports. The battery drawer is secured by a screw on the other 5D-series models (need a precision JIS cross point screwdriver to remove that screw... and care not to lose it!). The battery in there is something like a lithium CR2016 or CR2025 (a silver "watch" battery). These are widely available, once you know what's needed.
In order to fully reboot the camera, both the main and time/date batteries should be removed. Then turn the camera on and press the shutter release button once. The shutter won't fire, of course. But this should clear any residual power stored in the camera's ciruitry. Turn the camera off, put the batteries back in, turn the camera on and check the date/time. If they need to be reset, you got a proper "reboot".
If this works, I would recommend NOT using the Sigma lens on the camera. The problem you encountered might have been that lens isn't compatible with the camera. Unfortunately, this happens. Third party lens manufacturers older lenses sometimes simply won't work with newer camera models. Over the years this has happened a lot with Sigma lenses, though it usually only causes an Error code (which can be cleared by temporarily removing the main battery alone). But, who knows! It's a brand new camera model and there might be compatibility issues with third party lenses such as that Sigma. It's not likely, but possible that an incompatible lens might even do damage to the camera.
Only Canon lenses are guaranteed to work on Canon cameras. So it you get the camera working again, I'd just suggest not using the Sigma for now... only use your 24-70. Later you can check with Sigma to see if there are any known issues using that particular lens on the camera. And, if there is an issue, Sigma might offer a fix (re-chipping or new firmware, typically).
If the "reboot" doesn't work, it could be still have been a compatibility issue with the Sigma lens, but with some actual damage done. Or it might be a fault with the camera.
Can you still take shots focusing manually?
Have you tried using Live View focus (which I think is a separate AF system, from the viewfinder-based one)?
Hope this helps!
EDIT: I found an older article on one of the Canon websites that discusses the date/time battery and it's replacement on a number of Canon models. Check out http://cpn.canon-europe.com/content/education/infobank/batteries/care_of_batteries.do On the RH side of the page, part ways down, there are four pairs of photos showing the location of date/time batteries in different EOS cameras. The third pair of photos shows 5D or 5DII... which is where I'd think it most likely to be on 5DS/5DS-R, too, if the new cameras have a user-replaceable date/time battery.
I also need to mention that some of the more recent models have a built-in battery for this purpose that is not user replaceable. The 60D and, I think, 70D use a battery inside, on the main board of the camera. Only a tech can replace it, if needed. The above "reboot" method won't work on those cameras.
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Alan Myers
San Jose, Calif., USA
"Walk softly and carry a big lens."
GEAR: 5DII, 7D(x2), 50D(x3), some other cameras, various lenses & accessories
FLICKR & EXPOSUREMANAGER
