I have a Lenovo Z75-75 running Windows 10 Home. Some of the keys aren't working like the "e" and "o" keys and a few other keys. How can I tell if the problem is with the keyboard hardware or somethings else? Thanks.
In order to test if it is hardware or software (and it seems to be hardware), you can try a different operating system.
For this, try making a live linux USB. I would recommend Linux Mint, but Ubuntu etc. are fine as well. Mind you, a live Linux USB is the same thing as the Linux Installer, so do not get confused by that. Just do not install it, if you do not want to wipe you Windows. (In order to install it, you have to boot into Linux first, then click the "install Mint" (or whatever) program that you will find on the desktop.
If you have never done it, it might seem a bit intimidating. But it is not. Just watch a few youtube tutorials etc and you will find something. Even outside of this particular issue. Having a live Linux USB is very useful.
As to your problem:
If the keyboard works well on Linux, the hardware is OK. If it does not, and is broken in both Windows and Linux, it is likely the hardware, as the operating systems are very distinct.
Cheers.