Why doesn't my keyboard work on my laptop?

Maybe liquid damage? It's fairly common.

If not, it's also fairly common for them to just give up every now and then.

The good news is that they are fairly easily replaceable. Keyboard screws are usually located under the battery (actually in the battery void). There may also be one or two on the bottom casing and you may also have to remove the uppermost panel on the keyboard side (between the keyboard and the hinges).

Screws that hold the keyboard panel in place are clearly marked with a small keyboard symbol.

You can usually find a guide on YouTube (even if not the same model, you'll get a good idea how they fit together and I haven't come across any that are too dissimilar) or you can see if your model is on ifixit. Most of these Toshiba Satellite models have keyboard replacement tutorials (haven't checked them all but they should do)

Once the keyboard is out its a case of disconnecting the ribbon cable and installing a new one. You can usually find them on eBay pretty cheap.

Hope this helps!