P.,
It sounds like your son has gotten too attatched to the game boy. It is hard for some kids to put things like this down. Try using the gameboy as a reward. If you do your chores you will get it for X amount of time. If you don't behave like a "big boy" I will take it away for X amount of time. Soon he will learn that if he is good and does what he is asked he will be able to play with the gameboy. If he is showing signs of bad behavior, he will loose it.
I would start by taking it away at night just before bed time. When he gets up in the morning, he does his chores, eats, and gets ready for the day. If he does this, he gets it, but not for a long period of time. Start each day with 5 minutes, add 5 minutes for each chore he does, for getting ready, putting on shoes, sharing toys, doing homework, etc. If he misbehaves at school, daycare, or home, take away 5 minutes.
He will catch on quick. The more I do, the more time I get, the less I do, my bad behavior, I will loose it.
If that doesn't help, take it away for bad behavior, for the day. It might turn out that he is great for the rest of the week. Don't punish him for one bad day for two weeks. One-he will forget why he isn't allowed to have it. Everyone has a bad day once in a while and you shouldn't punish him for the entire two weeks for having a bad day. It would almost be like not getting a pay check because during that pay period you had a bad day, yelled at a client, told off a co-worker and had to work late one night. That would not be fair.
Try taking the game boy away for the next day, or the rest of the day, after he doesn't do his chores or has a bad attitude, or throws a temper tantrum. You never know, by rewarding him with extra time and taking it away for the behavior it might get better.
Good Luck!