Your process sounds mostly fine. Couple things here:
You shouldn't add water to liquid yeast, you should pitch it directly or make a starter before hand. You can find lots of info on here about yeast starters.
With your technique, you can top off like you did; it is fine as long as your water is sanitary. The most important part of cooling is getting it below 140 degrees quickly, which your chiller did fine.
It would help your sanity and your process if you used a hydrometer to take readings before fermentation and during the process. When you say there is no activity, that might not be accurate , and you can only really tell with a hydrometer. Your fermentor/airlock might not be sealed. It can also take 72 hours (or more) to show signs of fermentation, which many other posters on here will remind you.