I hate to say this, but possession of a template does NOT guarantee success to the AE newcomer. It could contain any number of expressions that prevent a straightforward replacement as you seek. It could have comps nested in comps nested in comps. At the moment, we have no way to tell.
Templates can have a high degree of complexity, but you're still unable to express your problem using AE's arcane terminology so everyone here can understand it.
If you have the luxury of time, I would scrutinize the WEALTH of information contained in the following link, to help you figure out what's wrong:
If you're on a deadline, get someone else who knows AE to take on the project for you. The chances are almost-certain that you'd miss the deadline.
Without seeing how the template is set up, it's hard to know where you're going wrong.
However, it sounds like you're copying nested precompositions, then changing the text inside and thinking that'll do it. You actually have to copy the compositions themselves in the project window and not the timeline window.
This sort of frustration can be avoided by going through these materials: Getting started with After Effects
They will get you the foundation you need to actually know what you are doing.