2008 MBPro Crashes when reinstalling Yosemite

My friend asked me to reset this old MBP to its original state so she could pass it on to her niece. The erase went ok. The re-install, not so much. It does the install, but then when the installer reboots, I get the attached error and it reboots itself. Then gets the same error and reboots, etc., etc., etc., until I have to shut it off lest it overheat. I am aware that there is an issue with the battery, however, it is plugged into the AC, so that should (IMHO) not be at issue, however, I'm stumped. As my personal MBP is much newer, I can't even create a boot USB for it as the machine can't run Big Sur and it's a ridiculous undertaking to make a Yosemite boot USB while running Big Sur. I've run a repair on all available disk drives, multiple times and attempted a reinstall multiple times. I'm seriously at a loss. Any help anyone can give would be greatly appreciated. (My personal opinion: send the dang thing in for recycling and buy her niece a lower cost iMac, but I don't think that's going to happen.)

Oh, and for the record: it would boot up and run just fine prior to my wiping it and doing the reinstall, so I'm not sure if I did something, or what I did uncovered a 'masked' problem that is only evident because I'm attempting to reinstall Yosemite.

Also, it had been upgraded to Catalina prior to the wipe/reinstall, so I'm not sure if that's causing an issue.

CTRL-OPTION-R did not allow me to boot from the internet (apparently the model is too old), so that's a no go. Neither did SHIFT-CTRL-OPTION-R. Turning it on and trying to run the Diagnostics didn't work either. (From what I read, hold the D after the chime until you see the progress bar...but this MBP doesn't 'chime' when you restart it, so it's a guessing game for me).

Again, any insight anyone can give me would be extremely helpful.

The last version of OS X that Apple released for a 2008 MacBook Pro is El Capitan (OS X 10.11.x). If this Mac was upgraded to Catalina, then this must have beed done using some sort of macOS patch. The original state for a 2008 MacBook Pro would be Leopard, but you seem to indicate you think this is Yosemite. There have been reports Yosemite failing to boot after installation do to expired certificates. You have give no indication where you acquired Yosemite. Perhaps your statement "it's a ridiculous undertaking to make a Yosemite boot USB while running Big Sur" means you used your Mac to create the bootable USB Yosemite installer. If true, this still does not indicate where the Yosemite files came from or the method used to create the installer.

Apple has a website How to get old versions of macOS. I assume these downloads have updated certificates. If you use your Mac running Big Sur to create the USB installer for El Capitan (or perhaps Yosemite) you will first have to install Big Sur in a virtual machine. I have tested this using a free version of VMware Fusion Player where the host was running Catalina. After creating the Install OS X El Capitan application in the Big Sur virtual machine, I would copy the Install OS X El Capitan application to the Big Sur host before following these instructions: How to create a bootable installer for macOS.

An alternative would to follow these instructions to create a bootable USB Snow Leopard installer. After installing Snow Leopard on the 2008 MacBook Pro, install the Mac OS X 10.6.8 Update Combo v1.1. Finally, use the 2008 MacBook Pro to create the Install OS X El Capitan application. You will need to use your Mac to do all the downloading.