Trying to wipe/reinstall an older iMac

My mother-in-law died, and I'm trying to do what one should do with her old (late-2009) iMac. I got as far as wiping the HD, then, starting into reinstalling the OS, got stuck. So, the disc is wiped, to the Mac is starting up to a choice of utilities, including "Install OS X Yosemite." I sign on to wi-fi. I select the icon for the appropriate drive, then click the arrow pointing to the right. I am prompted to sign in to the App Store

I see a box with the message, "Sign in to download from the App Store. Here is where I fail.

I have my mother-in-law's Apple ID and password, and I have used it to sign in to her Apple account. In doing so, I have seen that this computer is not associated with her account. It was originally a work computer, so maybe that's why. I also have my own Apple ID, but of course, this computer is not associated with my Apple ID, either. I don't think this is the problem however--at least not yet--since so far I haven't succeeded in signing in to the App Store. Keep reading.

When I attempt to sign in using either of these sets of credentials (after ensuring that the wi-fi connection is active), it simply doesn't work. Again, I've tried both my own Apple ID and my mother-in-law's Apple ID, both of which I've verified on other devices. When I try using my mother-in-law's credentials, I get a message saying, "Your Apple ID or Password is incorrect." When I try to use my own Apple ID and password, I get a message asking "Did you forget your password? Type your password followed by this code into the password field on your device," followed by a 6-digit code (on the other device), but there's no place to enter a 6-digit code.

Back on the old iMac, I can choose between "Cancel" and "Forgot password?" Clicking on the latter just takes me back to the starting point for reinstalling OS X Yosemite. Choosing the former achieves the same result.

So, short version, it seems I'm not succeeding in signing in to the App Store to download the OS software I wish to install, even though I have verified the credentials. (Just now, I tried again then verified that my credentials work from my own laptop to sign on to the App Store, but--to repeat--the iMac is not listed in my profile; nor is it listed in the profile of my mother-in-laws account.) I looked again to confirm that the iMac is still connected to the local wifi network. (I also have an ethernet cable plugged in, but it seems to be ignoring that. I know I'm online because when I use my own Apple ID, it pings my other devices with an alert and a six-digit code.)

What's my next step?