How to re-install OS X El Capitan after erasing HDD?

You will need a keyboard that produces the same code that the Option key produces on a Mac. What keys are on your keyboard to the left of the Space bar?

Depending on how you erased the disk - whether the volume or the physical drive - you may be able to do the following if you haven't tried already:

Install El Capitan or Later from Scratch

If possible, back up your files.

1. Restart the computer. Immediately, at or before the chime, hold down the Command and R keys until the Apple logo and progress bar appear. Wait until the Utility Menu appears.
2. Select Disk Utility from the Utility Menu and click on the Continue button.
3. When Disk Utility loads select the target drive (out-dented entry w/type and size info) from the Device list.
4. Click on the Erase button in Disk Utility's toolbar. A panel will drop down.
5. Set the partition scheme to GUID.
6. Set the Format type to APFS (SSDs only) or Mac OS Extended (Journaled.)
7. Click on the Apply button, then wait for the Done button to activate and click on it.
8. Quit Disk Utility and return to the Utility Menu.
9. Select Install OS X and click on the Continue button.

This procedure may require verification by prompting for an Apple ID and password of the previous owner. In this case, the procedure will not work.

You would then need to install Snow Leopard 10.6.6 or later, or Lion. Apple no longer sells a Snow Leopard disk.