MacBook Air (13", 2010) not responding when I try to reinstall macOS?

Your model is to old to support network recovery.

How To Do A Factory Reset

Selection A should be used on computers that came with Lion or later when factory new. These models had no disks included when new. Selection B is for Macs that came originally with Snow Leopard or earlier. These models shipped with Software Restore disks when new.

A. Factory reset of your Mac - Apple Support

B. Factory Reset Your Pre-Lion Mac Follow these instructions until you get to Step 6 of Factory reset of your Mac - Apple Support. At Step 5 you will need a Snow Leopard DVD or the installer disc that came with the computer.

1. 1. Boot the computer using the Snow Leopard Installer Disc or the Disc 1 that came with your computer.  Insert the disc into the optical drive and restart the computer. After the chime press and hold down the  "C" key.  Release the key when you see a small spinning gear appear below the dark gray Apple logo.
   2. After the installer loads select your language and click on the Continue button. When the menu bar appears select Disk Utility from the Utilities' menu. After Disk Utility loads select the hard drive entry from the left side list (out-dented entry - mfgr.'s ID and drive size.)  Click on the Partition tab in the Disk Utility main window.  Set the number of partitions to one (1) from the Partitions drop down menu, click on Options button and select GUID, click on OK, then set the format type to MacOS Extended (Journaled), then click on the Apply button.
   3. When the formatting has finished quit Disk Utility.  Proceed with the OS X installation and follow the directions included with the installer.
   4. If you are planning to sell or give your computer away, then do the following: After you reformat your hard drive and reinstall OS X, the computer restarts to a Welcome screen and asks you to choose a country or region. If you want to leave the Mac in an out-of-box state, don't continue with the setup of the system. Instead, press Command-Q to shut down the Mac. When the new owner turns on the Mac, the Setup Assistant will guide them through the setup process.

I tried this several times, with the Snow Leopard disc and it just pushed it out. I am glad I do not have any but time invested in this. I had also tried the other Option+ Command + R and Command R and just tried to go directly to the Utilities and erase.

All with little or no effect. Thank you for the links to what should work for this computer, I think I should look into a newer computer..