I took my guys to Disney last September and this past January for Homeschool Days and did it very inexpensively.
First, you need to decided if want to stay on Disney property. We typically stay offsite because we own a timeshare. We enjoy the extra space of condos and not having to eat Disney food every day. Yes, you must pay to park at the 4 theme parks, but it is still significantly cheaper than staying onsite. There are lots of timeshares and privately owned condos in Orlando which can be rented very cheaply, especially when you consider that some/all of your meals can be prepared there. We very rarely eat at Disney anymore, even bringing lunch/snacks in an insulated backpack that I found at Target.
Take a look at disboards.com...there's is a sub-forum for offsite stays and the people there are very helpful.
With that said, I was unable to book my January stay completely at our timeshare because it was a last minute trip. I was able to pick up a room at Pop Century for $60/night with taxes through Expedia. Disney wanted about $15/night more. And September is the lowest season of the year, so I would expect that you could pick up a room at a value resort in the $50-$60/night range.
As for tickets, if you book a package, only get the 1 day ticket that is required for the package. Disney's Youth Educational Services (Y.E.S.) offers a steep discount on park tickets. Also, the Y.E.S. tickets are all one price...no separate price for adults and children. In January I bought 8 day park hoppers with the plus option for $190/each. This gave us 8 park days at any park, the ability to hop between the parks, and 8 visits to Disney Quest and both Waterparks (in reality, that's 16 days of admission). The tickets are valid 7 days prior to your arrival date and 7 days after your departure date, so you can spread your trip over a longer time frame as well. We spent 16 days in Orlando, and were able to use our tickets during our entire stay.
We've visited Disney World at least 25 times in the past five years and never have we spent $2000 on a 4 night trip. Granted, our accommodations are "paid for" with the timeshare, but it can be done much more cheaply and with just as much "magic" than Disney wants you to know. If you have any other questions, or I can be of any other help, feel free to PM me.