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My hard drive uses the MacOS Journaled format. I put in a new logic board and every time I try to install High Sierra from a USB key , the installation goes as planned until it reboots. The problem is that the computer keeps rebooting indefinitely after a minute or so. I used internet recovery and it downloaded Yosemite (!). I guess it’s a matter of firmware, isn’t it? But it seems the only way to update the firmware is to install High Sierra, which the logic board doesn’t let me do. Is there a way I can solve this?

Depending on what you had on your system before as well as how you enabled OS recovery you will get the original OS the system had. Pressing Option & ⌘ and the R keys will get you the highest your system will support Review this T/N Mac startup key combinations and this T/N How to reinstall macOS from macOS Recovery