Why doesn't it work if I press more than two keys at the same time?

Read the Wikipedia article here: https://en.wikipedia.org/wiki/Rollover_(key)

In summary, your keyboard's electronics aren't designed to have more than one or two keys pressed at a time. Usually, these keyboards arrange things so keys common in normal typing and shortcuts used in business applications won't interfere with each other, but video games are another story. Special keyboards made for games will have "N-Key rollover," which means any combination of keys pressed together will work.

Some games, like Chrono Trigger, require you to press three keys at the same time to proceed in the game, in this case L+R+A. To get around this, you can temporarily change your keyboard mapping to something like CTRL for L, ALT for R, and Z for A. Since CTRL+ALT+(Any other key) has to be available on any keyboard for things like CTRL+ALT+Delete, this will always work.

The preferred alternative is to get a controller. If you have controllers for consoles like PS3, PS4, Xbox 360 (wired), or Xbox one, they will work on most operating systems if you plug them into a USB port.