So how would I do that?
No idea as I don't use it.
The JDK (or JDE) is available here
The reason why I'm confused is because on a different computer I ran the .jar file and it ran perfectly. The computer only had the regular Java downloaded though...
I can only tell you what I know and what I can observe.
The windows %PATH% should contain the directory of the Java JRE & the JDK (if you installed that too).
Recommend you compare the %PATH% of the system that works with that which does not.