Yup, sure do, Jestive… that question mark in the folder means your iMac can’t find a valid system folder to boot from, and it doesn’t support Internet Recovery… I see you tried to boot from the Recovery partition ( holding down command/Apple+ R together on startup) , not so good… anyways, what you should try to do before that is reset the SMC/PMU and zap pram 3-4 times on startup, before trying the built in Recovery Partition… here’s how to do that : https://www.macworld.com/article/224955/how-to-reset-a-macs-nvram-pram-and-smc.html#:~:text=Intel%20Macs&text=Press%20the%20power%20button%2C%20and,Mac%20to%20continue%20starting%20normally…. Then try the Recovery Partition ( command+R held down on startup as per usual) and see what that gets you… assuming your Recovery partition is good , you can also restart holding down the “Option” key which will get you the Startup Manager and the Recovery Partion should be listed there, use left and right and click to select the drive/ thing to start up from.. when in Recovery, after you’ve picked a language+ continued, moving your cursor to
the top centre of your screen will get you Mac OS X Tools ( Disk Utility, Terminal and a few other things) , then maybe run Disk Utility to verify your hard drive /storage is good and then Re-install the MacOS… make sure to set the startup drive as the Internal one when you’re done… hopefully it all goes well for you… if not, you’d have to make a bootable USB stick
with the MacOS installer on it, properly prepared, and boot from that, using the startup Manager command, and then plugging in
the usb stick, choosing it, and booting from
it. I’ve used LionDiskmaker X successfully in
the past to do that..but there may be other utilities that can do that on the Mac…
hope this helps you
John B