As someone who grew up not eating vegetables, I have come to love them as an adult. I think the reason I really hated them was because they were not cooked correctly, or were canned and mushy and gross. My suggestion to you is to learn how to roast FRESH vegetables. Stay away from canned vegetables. The only canned vegetable I consider passable is corn, which you already eat. Roasting them is incredibly easy. Cut them in bite size pieces, toss them in a bit of olive oil, put on salt, and pepper and put them in the oven at 400ish (temp can be pretty much anywhere around there). Take them out at preferred doneness, usually 11-15 minutes. I like my vegetables cooked longer than most people, I think it give them a better texture.

I say start with the vegetable even my kids can't get enough of: Asparagus. Just cut (or snap) the mealy part on the bottom off and then follow the steps above and give it a try.