Can't run Apple Diagnostics on 2011 iMac
I have a 2011 iMac running 10.13.6. I just booted it up for first time in I think 5 years. It's acting a bit strange, most notably boot pauses for a very long time, graphics seem very slow, and some weird screen refresh patterns when the desktop is first brought up. Activity Monitor showed some initial activity after boot (virus scans and the like), but that has settled down and I still see these issues.
The first thing I tried was to boot in safe mode by holding down the shift key, but that didn't seem to help with any of the issues.
Next thing I tried was booting with option-V to see what was going on during the boot delays, but that did not result in the expected verbose boot logging to the screen.
I then tried option-R for recovery mode. That did work, but there is nothing really there to help me diagnose the problems.
I then tried booting while holding D to run Apple Diagnostics, but like option-V it did nothing. I also tried cmd-D and option-D.
One other thing to note is that the I am using File Vault. So after a reboot I'm almost immediately prompted to provide credentials to unlock the disk, and then go through a very long reboot before being prompted for credentials again, this time to login. The login process is pretty quick at that point.
My question here is mostly what is going on with the boot keys? Why are some of them not working? Is there anything else I should be trying? Is there any other way to run Apple Diagnostics?