Finally wanting my birds to be happy

Hello guys!
I'm new here and I really hope you can help me.
Be ready for a lot of bad news.
My two boys are already 11 years old and I got them when I was very very young.
Neither me or my dad knew how to properly care for or train them and the people at the pet store gave the worst advice (they also treated them horribly).
Fast forward to now:
My birds are scared of basically everything.
They refuse to eat fruit or veggies, they will only eat seeds and I'm worried they'll get sick or overweight at some point because they don't get vitamins.
They are scared of my hand but they will eat from my hand.
They never come out of the cage so they never ever fly, we would leave the cage open for days but they are to scared to come out.
We let them out once when they were really young still but they flew away from us right away and wouldn't go back into the cage for a week, they hid on top of our curtains.
Since then they refused to leave the cage at all.
I can't touch or come near them, they don't bite but they run away immediately.
Same goes with toys, if we buy them toys to entertain them, they will hide in a corner of the cage and won't leave it for days, they won't even go eat so we have to take them back out.
Apart from those negatives, my boys are completely healthy and always seem happy and comfortable in our company as long as we don't get to close to them.
They eat with us, sing, fluff up a lot and nap next to us.
They don't whistle melodies or talk at all though.
They don't show signs of fear or aggression unless we try to train them.
I would love some advice on how to help them be happier, I want them to be able to fly around in the room but they should come back to me or the cage and not hide in a high place for a week.
I also want them to be more comfortable with my hand, I want them to be able to step up without being scared.
Also, what can I do to make them less scared of new foods and toys?
They must be so bored without any toys but I can't let them starve for days every time I introduce a toy!

Ps: I tried many things, putting my hand in the cage a few times a day, talking to them lots, giving them lots of attention, moving slowly, rewarding them for little things, even things like blow on their faces or spray them with water.
Nothing seems to work and I know it won't be easy to redo 10 years of almost no training but they deserve to be happy and I want to try my best to make that happen.
Thank you for your help in advance!