Toilet Tank slow leak, have all new parts, tried all troubleshooting...help!
If your tank is constantly leaking water, but you've not found it anywhere, then it is nigh on certain that it's going into the toilet bowl. Tester101's tip of putting food colouring into the tank and seeing if it appears in the bowl will likely confirm this.

The issue is then to find exactly where the leak is. Either your flapper isn't closing properly, there's a leaky joint where the overflow pipe connects (just below the flapper), or the seal between the flapper apparatus and the tank isn't watertight.

I would hazard a guess at it being the seal between the flapper apparatus and the tank, probably due to either under-tightening or over-tightening when installing the new flush. Over-tightening is perhaps the more likely - it shouldn't be tightened too much or you will distort the rubber seal.