
You can download your Mac’s OS installer (in my case High Sierra) from the Max App Store (or another official Apple site). I think my Time Machine disk for that machine was bootable but I don’t remember. You will need a bootable drive of some sort (actual hard drive or USB). Long long whole day story short: Some of this had to do with the switchover to APFS in High Sierra, which won’t apply to you but it might get you over the hump. I also couldn’t boot into Online Recovery Mode (or whatever it’s called). I could launch into Recovery Mode but trying to reinstall the OS failed near the end when it said it couldn’t partition the drive. After I nuked the drive with Disk Utility, I found I couldn’t boot the machine.

I transferred the data to my new machine with Migration Assistant and I have a bootable clone of the hard drive. I recently finally replaced my 2009 iMac and wanted to wipe it clean. I ran into a similar solution just last week.
