Hi,
Issue might be the Apple ID/Account mismatch (ID that was used before on this Mac, and the one you are using right now should be same).
there are two possible ways to fix it:
1) use USB installer, i can prepare a USB for you with latest version supported by A1342 macOS High Sierra, for this you need an external USB and another computer to prepare Boot Media
2) we can try the Internet recovery this will install version of macOS that was factory-preloaded on your Mac, this won't need any extra USB or computer to work but you need working internet connection. and you can update macOS later from AppStore as the all the recent versions of macOS are free to install.
**Edit: just completed a similar project for MacBook Air (2010) A1369, you can check review Section.
Please contact me in chat to discuss more.
Regards,
Hamza