On your Garmin you can choose to include or exclude zeros in the power average. The 'real' power average is the one that includes zeros in the average. Normalized power is useful for giving the 'cost' of highly variable efforts such as racing where you may spend quite a bit of time free-wheeling, but then ride hard. The true average (including zeros) doesn't necessarily reflect how difficult the effort is. Normalized power does.
I'm not familiar with Ascent, but you might want to have a look at Golden Cheetah for free, but brilliant analysis software. The official release
is good, but the development builds
are way better (even if there is still the odd bug or two).