Apple - Cannot reinstall OS X. Will Apple Store do it on the spot?

On startup hold Command+Option+R. You can now use Internet Recovery to install OS X. Don't download from shady sites. You are compromising your security this way.

I had to download one for El Capitan from a shady website.

Eeek. I would not trust that, personally.

Do you have access to a good internet connection? If so, you can use OS X Internet Recovery to install a fresh version of Mac OS X via your internet connection, directly from Apple.

YES! You can either make a Genius Bar appointment or you can do a walk-in. If you do a walk-in for the genius bar you may have to wait a bit, but they will do it for free. The instillation may take a little while, so plan on having some free time and a good book (or movie or something - there's free in-store wifi).

Each store typically has good internet and a local caching sever, so you are loading your OS Recovery and install images from the local network which makes it quite fast. Having the Genius Bar close by is just bonus if you don't know what to do or need advanced cleanup.