I wouldn't start again. I wouldn't perform any water changes either, not until the cycle has finished.
You should see ammonia rise, then nitrite rise, then nitrate rise over time.
Bacteria will grow and consume the ammonia, producing nitrite, other bacteria will consume the nitrite, producing nitrate.
Nitrate must be removed by water changes, but that is only important just before adding fish (and then as part of regular maintenance, e.g. weekly).
I have never used fish food (to cycle), but it does work, the only question is how much ammonia (and therefore how much bacteria) it will produce. I would have thought not a lot. I would also have thought that you should add the food every day, rather than every-other.
How much did the ammonia shoot up to before falling to zero?
This method might produce enough bacteria to handle a small load of fish to start with, after the ammonia and nitrite are at zero, and following a large water change (approx 50%) to bring nitrates down to about 20 or less.
I just had a quick search and couldn't find any posts about cycling with food, but there are some around. Hopefully someone can give a better idea of how long it will take and how effective it will be.
The main thing with cycling is to be patient, as it can take a few weeks of looking at an empty tank unfortunately.
Another thing you could do is get some filter media or gravel from an existing tank. Your LFS sound okay, maybe they would give you some? You can add some mature gravel in a stocking if you want to be able to remove it afterwards. If you can get a fair ammount of mature filter media and put it into your filter then the tank will be immediately seeded with bacteria and you could (in fact should to avoid bacteria dying) add some fish right away if the water tests okay.
