One some older Mac’s some issue can install with the automatic installation when you boot with Option-R / Option-Shift-R.
A possible workaround is to make an internet install on an external disk and then let the installation start from that.
- Start your Mac holding down Command + R.
- Prepare a clean external drive (at least 10 GB of storage).
- Within OS X Utilities, choose Reinstall OS X.
- Select external drive as a source.
Your Mac will restart and make the installation…
Thanks to this site.