It's so frustrating, isn't it?
This won't help with the veggies, but I make fruit smoothies for my girls. And when they refuse the fruit smoothie (which oldest dd sometimes does, out of suspicion that it is good for her! LOL), we put food colouring in it and then freeze it into a popsicle.
Then, all of a sudden, it is the yummiest thing in the world and they both inhale them! Good way to get lots of exotic fruits into them.
As for the vegetables...I find that when my daughters will try things, they will usually decide they like them (example - youngest dd really disliked both ketchup and taramasalata the first few times she tried them...but oldest dd loves both and ate both in front of youngest dd...who kept trying until now she loves them as well!).
So...my suggestion is to just eat the vegetables yourself in front of your dd. Talk about how yummy they are, but dont' offer to her. Maybe do the same with other non-veggie things, so you confuse her.
With mine, they'll eventually ask...and often they'll then decide they like it (if not, keep eating in front of her and letting her taste when she is interested - often tastes are acquired).
Try not to let her know how much it bothers you that she doesn't eat all the veggies you'd like her to eat. They LOVE to have that little bit of control (and will refuse something they love if they know you want them to like it!).
Good luck...hope someone else has other ideas.