Disk Utility can't load disks in Recovery Mode
Trying to wipe an old Macbook - late 2013, 15 inch, Intel chip. I start it in Recovery Mode, then go to launch Disk Utility. There, it just hangs - the spinner spins around happily, but the disks never load, even after an hour.
I've tried resetting the NVRAM and the SMC in different order, and tried using the Internet Recovery mode. All with no change in status. I also tried to just reinstall the OS to see if that might help, and that just hung as well. Tried booting into Safe Mode, but the computer just shuts down when the progress bar is halfway across the screen each time. So now I'm kinda at a loss.
Thanks in advance for any help!
MacBook Pro Retina