Claudia, its not your water for one and neither lack of nutritions. For the "specifically for growing plants" I actually spent some time just the other day at a chain petstore looking at their lights (cause mine are all set up from the home store), and I came to notice there's one bulb sold as "plant lamp" that's totally impropper spectrum for growing plants.
If you chose to try plants again I'd suggest a flourecent that is 1) Full Spectrum 2) Rated around 5-6500 Kelvin 3) And guessing you have a 28g tank on your hands, I'd get something like a 35-40w bulb over it.
Then once you run out of the current fert you're having I'd try a different brand, pers I'd get Seachem's "Flourish" a comprehensive all in 1 liquid fert. And continue the root sticks for the Swords.
From what you're saying, I am honestly convinced it was your lights that 'broke' you on the old set up.
The tall grass like you have there may be Vallisneria type Vallisneria
For your new set up there 2x 96 watts over a 60gallon tank is too much IMO for the plants. For comparison I run 2x30w over my 55g's. Higher wattage will not make up for lack of spectrum and that's where many planted set ups fail. And with a proper stock of fish there'll be sufficient CO2 to not need add CO2.
Any set up will need to be balanced between the lights- CO2- Nutrition. If you have for example super high end light, you'll then also need more CO2 and more ferts. Contrary the lower end set ups like Byron's or mine with full spectrum lights like from GE, Phillips etc do fine with little fertilizers to non and no CO2 systems. And I think both of our tank pictures with the plants speak for themselves there