On My Old laptop runnig Office 2010 Professional 32-bit I had the following that worked fine:
Created a template document
- Added a macro to normal.dotm, a hot-key that created a new document from that macro.
- Edited the settings in security center to activate all macros so that I wouldn't get security warnings about my normal.dotm

A couple of weeks ago my 3-year old laptop crashed so I bought a new one. I recreated the same setup. I copied normat.dotm and my template .dotx from the hard drive of my old laptop to my new one.
It worked but I got macro warnings so. I went to the security center and activated all macros on my new computer.

Now I can start word without it giving me warnings about the macros in my normal.dotm.
I can press the shortkey that creates a new document from my template.
I can start typing in my new document.
When I save my document ctrl+s the document saves fine.

Here's the difference:

I get a dialog box asking me if I want to save the changes in the template as well.

This never happened on my old laptop.

I also did a test with another template that I had and got the same behaviour. So I don't think the problem is related to the template.

It may be related to normat.dotm or some security settings in Word-