Sorry... I am a bit confused, so please help me understand the situation.
You have been cycling for a while... I see you say a month... in that time, nitrite should be showing up... so something is amiss.
How often are you doing ammonia currently?
2.0 ppm ammonia drops to 0 in 24 hours means that nitrite should be showing up in some capacity - or had... at some point. Did you ever get a color in the nitrite tube other than the 'baby blue' color representing zero? Or are you getting a 'greyish' color?
Nitrates keep popping at 80ppm... again, the only way nitrate would show up without nitrites would be if you have a complete cycle going OR your tap water is exceedingly high nitrate.
One other possibility remains...
The ammonia is processing to nitrite, but has well exceeded the tolerance of the test kit, and it is giving you the 'greyish' color, rather than the blue. That represents 'off the scale'. And a side effect of that can be, that you are getting a false high reading in the nitrate, because the test kit converts the nitrate to nitrite (Bottle 1, I believe) and then Bottle 2 is reading the nitrite in the tube. And if you have a nitrite SPIKE, you might very well just be reading that with the nitrate test (as its capable of reading higher values than the nitrite).
If all this is true, and you've been cycling for a while... getting the 'grey' color, you may have stalled the nitrite portion of the cycle and require a full tank water change to remove them. Then, before adding ammonia... do a nitrite test, to see if that brings the nitrite down low enough to be on the scale.
A secondary option for testing would be a diluted nitrite test. You can take a sample of tank water. Add 9 x as much water from your tap to that and mix them. Then test that sample of water. Whatever nitrite reading you get, can be multiplied by 10 to get a decent sense for where the nitrite really is. Our goal is to always have it well under 15ppm, as that's normally around where it stalls.