I don't like carrots or celery either....though I love THIS carrot!
Mostly what you all said is what I'm going to say. I eat a lot of salads...shredded lettuce with Feta or romaine with low fat cheese and grilled chicken are my favorites. I also like broccoli and every now and then french green beans. Mushrooms and cucumbers are good plain or with salads. If you don't like any of that...I think the suggestion of drinking V8 is great advice.
I also can eat tomato if it's diced up in a salad or soup or toasted on bread with low fat cheese....trick yourself into eating it and you might just find out you like some veggies. Hope this helps! Good luck.