Thank you for the second last post of yours...
I will follow that...
That's a new one on me, my understanding is that the regulator shouldn't require all that hardware on the output side. If the input voltage was bad enough to need an LC pi filter, I'd put it on the input side. Give the regulator relatively decent input and it will do its thing just fine.
But I will not agree with you in this...
I tried a lipo battery on the input of the 7805 which had the cleanest input with no noise but then still the 7805 generated a noisy output...
So I believe that the 7805 itself is generating some rippls which is generating noise on the analog pins of the atmega...