Hi, Jeffwillcreg, yes, I agree, you're in a very tuff situation right now, as you don't have the time (and money) to get your iMac fixed. Hopefully, Me (and US, all of us Mac users here) can help you do that...
first off, that flashing question mark thing means your iMac and Mac OS can't find a valid system folder to boot up from.... secondly, you are trying to (I believe) try to do Internet Recovery--Command+Option+R, and your iMac may be too old to do that....no worries, I have a Classic Mac Pro 5,1 and I can't do that either...so that leaves either using the built in Recovery Partition which you can get to by rebooting and holding down the Apple (Command)+R keys together on startup... before you try to access the built in Recovery partition, you should reset the smc/ PMU and zap pram 4 times on startup, as per this link, it couldn't hurt, anyways...::->https://www.macworld.com/article/224955/how-to-reset-a-macs-nvram-pram-and-smc.html
THEN
after doing that, then try to access the built in Recovery Partition by restarting and holding down Apple+R keys together on startup....if you see a language selection screen, it worked....pick one and continue...to get to Mac OS X tools, which you may need, move your cursor to the top center (centre) of your screen and click, Mac OS X Tools should now show up.. .Run Disk Utility.... see if you can re-install the Mac OS from the Recovery Partition.... if so, great, make sure your built in drive (hard drive or SSD) is set as the Startup/Boot Drive just as you finish. It doesn't pick that automatically, it isn't the default, so you have to do that, because if you don't, you'll boot up to the Recovery Partition or whatever which is not really what you want, is it??? Otherwise, you'd have to make a Mac OS X Bootable USB stick/Flash drive/thumb drive with a copy of the High Sierra Installer on it, or at least Sierra....maybe Snow Leopard would do in an emergency.... anyways, you'll need a copy of the installer (MacOS) plus a properly Mac formatted USB stick of at least 8 gigs capacity/size but 16 gigs is better, and you'd probably need to borrow/use someone else's Mac to do this on.... it is, I suppose, technically possible to do it all in Windows, but I have no idea how right now... anyways, here's a link to High Sierra installer:->How to download and install macOS - Apple Support (CA)
that link covers from Lion (Mac OS 10.7 ) to Ventura, Mac OS 13) which is pretty much all of 'em....
good luck
John B