Well I see everyone is helping you out. Well to be honest your budget is really gonna dampen a lot of options for you. It's always good to look around the net for used gear if your limited to a tight budget. Check the marketplace here on scuba boards, also check ebay, and leave some info with guys like Mike at H2O Photo Pro's, sometimes they run across some pretty good bargain used stuff. IMHO if your limited to $2000.00 and you want HD rig for underwater. Go with a lower end Sony or Canon that is a model thats a year or two old, such as the Sony HC line, or Canon HG or HV series. You can usually find some pretty good deals on the older models. And to be honest, most of them are all around the same quality. You just need to watch there low light ability, especially since your budget is gonna limit your lights. As far as housing, your really gonna be limited due to the budget, but I would look at Ikelite, especially if your going with an older model camera, you can usually get some decent deals. Lighting, to save on your budget there are some halogen and HID dive lights that can be converted to a video light, for example you can use the UK Light Canon 100 for a video light, and if you search around you can find the light for about $175.00 then you just need an adapter to mount it.
You have some options, thats for sure, but your gonna be right at or slightly over your budget. Let me ask you this, What do you want the video for? Is it just for your own viewing pleasure? There are some pretty decent set-ups out there that are lower resolution, but will give you some pretty good 720p output, such as the Bonika, and all for around $700.00 or so. You need to also think about what your willing to give up to meet your budget. Some of the underwater video stuff, you can buy in stages. For example, you can buy the camera and housing and wait for lights as long as your not going deeper then say 60 - 80' depending on the water type. After about 60' your gonna loose some, well most color. Not that some of that can't be corrected in post.
How about giving us some more information. Where is most of your diving going to be? What kind of computer, PC or MAC? Green water or Blue water? Wide angle open water shots or close up macro shot? And if this is just for your personal viewing, or web broadcasting? I will also look around the net and see what kind of deals are out there, and maybe give you some options. But a lot of people on the boards here will give you some pretty dam good advise. In fact Robin, I believe has a few rigs and is really good with the Ikelite housings. Ron and Mike have some really awesome experience and will always be honest and point you in the right direction.
And someone mentioned the Canon HF-S10, the best consumer camera out there right now. But thats gonna put you way way over your budget. Even the little brother HF-S100 is gonna hurt you. Your looking at $1000.00 for the little brother HF-S100, another $2500.00 - $4,000.00 for the housing (excluding Ikelite, they still haven't advised me when there housing will be ready but I expect in a month and probably around $1600.00). And as I said lighting you can wait a little while for that, till you can raise more funds, unless you go with something like the light canon, which by the way I have used and still have them for video lights, the work pretty dam good for $200.00.