My battery died while El Capitan was installing Like it says above, my battery died. And when I charged it again it din't work. I logged in, and while it's charging it just restarts again, and again, and again.
I tried reinstalling the OS, but my macbook wont connect to any internet. And because it's a MacBook Air, it doesn't have a adapter (I'm not sure how to call it), for the internet.
You can do Internet Recovery using a WiFi connection, if available. 

If not, you have two other options:

1) Purchase an ethernet adapter and connect directly to your modem or router and perform the Internet Recovery.

2) If you have another Mac, you can download the OS and copy it onto a USB drive and install it on your MacBook Air.