Well I cant really tell you why your turtle died. Tell us more about the setup, size, how many turtles, ect. Greens and ham isnt very nutrionial at all. First off there hatchlings so they need protien. Go to the petstore and buy a good pellet good. Either Mazuri (the best) or Reptomin. Also, while you are out buy a dozen or so feeder fish (rosies or guppies, NOT goldfish) for them to eat. Just put them in the tank, and they will chase them and catch them. You can continue feeding the greens like Romaine lettuce but only everyother day. Feed the pellets everyday, and always try to have some feeder fish in there tank.
About the filter... I would reccomend a HOT Magnum 250. It is a great canister filter that hangs on the back of your tank like a powerfilter. It is about $45 if you click on the link...
Chris
HOT Magnum 250
-----
0.1 Red Eared Slider, 1.0 Common Snapper, 1.0 Bearded Dragon and a 55gal Native Fish Tank with a 6in LM Bass, 3 Crawdads and a Pleco.
I use to have a collection of Leopard Geckos that I bred, but have sold them.