Good for you for not giving up!
What in particular are you looking for? Both fruits & vegetables?
Fruit: Raspberries seem pretty easy-going to me. Fruit trees too, just remember to keep them well watered for the first few years.
Vegetables: Radishes, "wild" green mixes, potatoes, squashes, peas/beans.
Those are suggestions based upon my opinion, others may disagree or have other suggestions.
I'd say start relatively small and try to research what each crop needs to be healthiest. Often the hard-to-grow plants are just more picky and if you learn what they like best and try to provide it, they aren't really that hard to grow after all.
Starting small is good, because it allows you to be more attentive, which I think is often the key to having a green thumb (having the time to hover over your plants, if need be).
Good luck and keep trying!