Cycling problems driving me INSANE

I am on day 40 (40!) of trying to cycle a new 55 gallon tank with fish. I have tested my water every single day (sometimes twice a day). I started out with Mardel 5-in-1 test strips and am now using the API Master Test Kit; have not noticed significant differences between the two. Yes, I shake the bottles really well. No, the test kits are not expired. Yes, I condition my water with Prime; maintain the same temperature +/- 1 degree during water changes; rinse filters in old tank water in bucket during water changes (using same filters since tank start-up); maintain tank temperature of 78-79 degrees consistently.

Here are my wacky readings.

Day 1-20: ammonia 0, nitrite 0, nitrate 0. No water changes.

Day 21-26: ammonia 0, nitrite 0.5, nitrate 0. Did 15% water change on days 22 and 24 and vacuumed about a third of the gravel both times.

Day 27: ammonia 0, nitrite 1, nitrate 0. Did a 25% water change and vacuumed a third of the gravel.

Day 28: ammonia 0, nitrite 0.5, nitrate 0. No water change.

Day 29: ammonia 0, nitrite 0.75 (between 0.5 and 1 color-wise), nitrate 0. No water change.

Day 30: ammonia 0.25 (first positive ammonia reading ever), nitrite 1, nitrate 0. Did a 50% water change and vacuumed a third of the gravel. Took water to the LFS after the water change and they said ammonia and nitrites were both reading 0.25.

Day 31-38: ammonia 0, nitrite 0.5, nitrate 0. No water changes (as nitrites not rising). Brown algae began to appear on the fake plants and the filter uptake around day 35.

Day 39: ammonia 0, nitrite 0.25, nitrate 0. No water change.

Day 40 (today): ammonia 0, nitrite 0, nitrate 0. Double checked result with the Mardel 5-in-1 test strips; same results. It might as well be day 1!

What is going on?? Where do I go from here? <sob>

Yes I have, and my untreated tap water has no nitrites. Just rechecked the tap again--still no nitrites.

Weezer, I have a liquid test kit and nitrites, nitrates and ammonia are all zero as if it were day 1 instead of 40. Could you explain to me how waiting two more weeks will make my nitrates rise if I have no nitrite to feed the bacteria?

HD3, my LFS has been out of Bio Spira for weeks now. Anyway, my ammonia and nitrites are zero with 10 days of fish crud in there and no water changes so I must have the bacteria that converts ammonia to nitrite in there (which is what Bio Spira contains, or so I've read). My problem is I don't have the bacteria that converts nitrite to nitrate, and now for some puzzling reason I have no nitrite to feed that sort of bacteria anyway, even though I haven't cleaned the tank in over a week!

What can I do to get the second part of the cycle going?

I feel sick...:sad:

No water changes for past 10 days, Weeser. So your nitrites dropped to zero with no nitrates also??