have you tried not forcing them to eat the vegetables? It is hugely stressful for everyone when food becomes a battle ground. I don't make my 2 eat anything (now - though I am times tempted belive me, but it's virtully impossible), but I do insist they try it (and DD1 has agreed to that - DD2 is too young), and I don't serve anything else to make up for the vege they don't eat. if they reject dinner completely and they are really hungry they have the option of plain toast. I really don't want food to become a control issue (esp with girls) so I try very hard to stay as neutral as possible about it.
When DD1 stops eating and leaves veggies I often ask her to eat just 5 mouthfuls of her veges - she will do this if there is a mango or something else she loves for afters. Yes it's bribery but it works,
Also when DD1 was in a VERY fussy stage she would always eat cucumber and carrot sticks - so while I cooked dinner I would give her these to munch on. I add in radish, sweet pepper strips, cherry toms, mange tout etc on rotation - often rejected but sometimes eaten. It takes pressure off eating the vege with the meals if they have eaten these beforehand - and if they are hungry waiting for dinner you might be surprised. In the past there have been times when the only vege DD1 will eat is cucumber - we go through several per week. My 2 actually can have fights over cucumber 
Simply changing the carbs to wholegrain version can make a difference too and they will get used to it. Wholegrains have fiber, trace elements/minerals and oils. Brown basmati rice is really nice, whole grain breads, you can get wholegrain Jacobs crackers now. You can buy lots of wholegrain pasta in supermarket.
They might protest for a while, but they will not starve.
Re the X-box suggestion, maybe the only way they can earn X-box time is by eating vegetables? X minutes for trying, X minutes for eating, X minutes for 5 mouthfuls etc. Then it becomes part of their area of control and they can decide for themselves.
I would think the vege would soon become 2nd nature as they got used to it and you wouldn't have to do this for too long?