For example, using US airways vacations you can Fly RT from Chicago with one stop and stay at Hyatt Regency Wakiki Beach for $1,550 per person from Jan 11-18 (Sunday through Sunday). This was just after a quick search. I am sure you could even get a little cheaper. Or you can stay at a cheaper hotel.
It's doable for flights/hotel for 2 people to go to Hawaii for a week on your budget. You can post in the Need Help Finding ... threads for more specific help.