Hurrah for minimal tech--my favorite.
Seriously, out of 13 tanks in the house, I've only got filters on 3 of 'em.
Frogbit can take awhile to find it's footing in a new tank but if you don't start seeing some new growth, two main things to consider are lighting and fertilizers.
You might not be getting enough light, especially if the indirect sunlight you're getting doesn't hit at enough of an angle to illuminate the TOP of the leaves. Side light does little for these guys. Not sure what bulb you have, but consider switching it out for a 6500k bulb. No need to order from an aquarium place, just start sleuthing the lighting aisle at Home Depot (or your local equivalent).
In terms of nutrients, I've not found frogbit to be particularly choosy. Any reasonable liquid fertilizer dosed daily will go a long ways to keeping them lush, but with such a low bioload you'll want to do at least some supplemental ferts.