Why is my keyboard broken

In your case, it sounds like the keyboard matrix is bad so the laptop needs a new keyboard. Try an external and see; if it's not present, the internal keyboard is bad.

The challenge is finding parts. Toshiba was always difficult to get parts for (without pulling them from a dead laptop) and also used the DMCA to take down service manuals and hasn't given me a good reason to let my grudge go, even under Dynabook. I would see if you can find a laptop with a dead motherboard or another major fault like the screen and get it from that; that will be your best bet since from the little info on Toshiba laptops that exists, it may be integrated into the palmrest. On the other hand, this IS from 2015; it may be worth considering a new laptop that isn't a disaster to repair in terms of parts availability because the situation ain't getting better with Toshiba as parts stop being produced for these older models.
In terms of parts availability, HP (read: business class, not consumer grade) is probably the best these days, but Dell is a close runner-up; they just funnel anything that isn't a wireless card, RAM, or SSD through 3rd parties like PartsPeople, whereas HP will directly sell most parts to you. Dynabook even shut down the Encompass parts portal Toshiba had sold the few parts they let customers replace and it goes to a NXDOMAIN error now. Too little too late for Dynabook IMO.