Unknown hardware issue, old Macbook Pro

I would first check the health of the hard drive. You can try connecting the drive to your other Mac and running DriveDx to check the health of the drive. You will need to install the special USB driver so that DriveDx can communicate properly with the external drive. However, some USB controllers found on USB adapters, drive docks, and enclosures may not allow the necessary communication even with the special USB driver.

Another option is to create a bootable Knoppix Linux USB drive using Etcher (Mac/Windows/Linux). Option Boot the Knoppix USB drive and select the orange icon labeled "EFI". While Knoppix is booting the Mac may appear to be frozen on the boot picker menu so give Knoppix lots of time to finish booting.

If Knoppix boots to the desktop, then click on the "Start" menu icon on the lower left corner of the Taskbar and navigate the menus to "System Tools ---> GSmartControl". Within the GSmartControl app double-click on the hard drive icon to access the drive's health information. Post the whole report here so I can examine it. GSmartControl also allows you to run the drive's internal self diagnostics. The short selftest takes about 2 minutes to run while the long/extended selftest can take hours or even a day to run depending on the size of the drive.

If Knoppix fails to boot to the desktop, but insteads provides you a command prompt (black screen with white text), then let me know as I can provide easy instructions to access the drive's health information.

Another advantage to booting Knoppix is it is an easy way to test out the hardware. Usually if Knoppix won't boot properly it will indicate a hardware issue.

So you are not experiencing any issues with the drive connected externally? Is it a hard drive or an SSD?

Checking the health of a drive is an easy way to mostly eliminate the drive itself as the source of the problem plus drives tend to be a weak link. Plus it may also be able to tell us if you have a defective cable. Plus Knoppix uses a lot of memory to run so if Knoppix has problems as well it could indicate a memory issue.

If you can boot the drive externally, then I would recommend also running EtreCheck to look for software issues. Post the report here using the "Additional Text" icon which looks like a piece of paper.

Instead of restoring from a backup which can bring back your software issues, you may want to perform a clean reinstall of macOS by first erasing the physical drive (at least for testing purposes as this will help determine if the issue is hardware or software).

If it does not seem to be causing the problem, then I suggest you are making good progress on the Internal drive issue, likely the cable (they are a weak point in these MacBook Pro models).

Maybe that other diagnostic-reported error is temporary -- regardless, it appears to be unrelated.

4SNS/1/40000000: TB3T-128.000

That sensor error. Sensor reading 0 or nearly a power-of-two [exactly like your 128 reading] sometimes indicates the sensor has completely failed or is disconnected.

My recollection it the T indicates temperature sensor, and B battery. ¿Is that possible?

Glad we could help and it was such an easy fix.