I forgot to add water conditioner in tap water..

Since you haven't added any ammonia at all, and you got a reading of ammonia and nitrite. My best guess is that the live rock is no longer live. All the organic stuff came with it are producing ammonia now because they are all dead from the chlorine you had in your untreated tap water.

On the other hand, you added Bio-spira a few days later. Chlorine in the water could be gone by then, thus Bio-spira might be working just fine. The reading of nitrite is an indication of an incomplete nitrogen cycle is underway.

If the above case is true, then you shouldn't have started over. Just wait for the tank to get cycled. Once you get 0ppm readings on both ammonia and nitrite, you may add a new live rock.