I don't want to just implement a more comprehensive physics engine that already exists like Box2D
Unfortunately that's probably what you'll end up doing, and you'll spend alot of time doing it! I've tried to create a complete solution and it's not easy! You'll wonder where the last 12 months went
Creating a simple engine where a few objects will collide and bounce off each other isn't too bad, here's a good resource for that. If you start using lots of bodies however the calculations get pretty tricky.
I don't want to just implement a more comprehensive physics engine that already exists like Box2D and just disabling rotation on every body as it has so many extras that I won't be using that will be wasting valuable processing time
I don't think you'll waste much processing time at all having rotational code there. But if you really insist then Box2D is open source so you could always just take out any rotational code?