We have been seeing reports on this forum where it appears Apple may have turned off the servers supplying the macOS online installers for the older Macs.
You can try booting into Recovery Mode using Command + Option + R which theoretically should bypass the App Store authentication.
You may need to use an OS X 10.6 Snow Leopard retail upgrade DVD (the one with the picture of a snow leopard on it), then make sure to install the latest 10.6.x update patches. Then you can download, extract the macOS 10.11 El Capitan installer to the Applications folder. Then you can run the macOS 10.11 El Capitan installer from the Applications folder, or create a bootable macOS 10.11 USB installer. You may need to download the macOS 10.11 installer .dmg file using another computer (any computer or OS capable of accessing the Internet & the Apple website.....then transfer the .dmg file to the 2009 laptop where you extract the real installer from the .dmg file.
If you have access to another Mac compatible with macOS 10.11, then you can use it to create the bootable macOS 10.11 USB installer.
Edit: Generally a compatible Mac for macOS 10.11 is one from 2007 to 2015. You can use this article to confirm:
https://eshop.macsales.com/guides/Mac_OS_X_Compatibility