You don't have any CYA, (aka stabilizer), which is allowing your cl to be eaten up by the sunlight. You need to find out if any stabilizer was added to your pool at startup. If so, after a week or so you should be able to see a Cl residual. if not, you need to get some stabilizer and add it to your pool, through the skimmer, and not retest for it or backwash for at least a week until it completely dissolves.

I don't know much about the Hamilton index, but trichlor tabs are very acidic, and I can see where it would be impossible to run a high pH pool if you're using trichlor!

Janet