For $4/500 you probably won't be able to afford to rent the genny you'd need for big lighting units... on top of the lights and the proper distro and someone qualified to run it.. plus the gas; a 5K, for example pulls 50 paper amps, remember, Watts=Volts*Amps. So in this case, you know the Watts, 5000, and the volts, 100 (rounding here to make it easier and give you some head room to deal with line loss ect), so you need to figure out the amps... 5000=100*x? well 5000/100=50 so 5000W=100v*50a. I know the math is basic, but this is important to understand when you start shopping around for gennies. So to even begin to light this with tungsten you'll need a genny where you can come out on 100A legs and then split that off through a distro system. I am assuming you haven't used a genny like this before, and as such I HIGHLY advise you don't do it, or you hire someone who knows what they are doing. Electricity Kills, and a distro system from a genny is most certainly not plug and play.
Now, onto how to do this on the cheaper. Depending where the house is located, it would probably be simplest to gel the windows with full CTO, which will give you the orange, balance to daylight on the camera, and bounce light in with shiny boards. Then you just have to blow out the windows, which shouldn't be too substantially difficult on a digital camera.
The room is smoked/hazed, yes, and for the interior lighting I would rent some kinos and maybe a few small HMIs to match color temperature outside and provide you with fill
You'll want to shoot all the performance stuff quickly as the sun moves, but it's not that fast-- just have someone to reposition the shiny boards as you go.
If you want shafts of light, look into HMI PARs, 1.2Ks should be good. Now on HMI they don't pull as many amps as their wattage suggests. A 1.2K HMI will pull more than 12amps for example. I don't know the amperage off hand, but it is listed on the ballast. If you are powering from the location; you'll want to lay out the circuits.
Get a boom-box, plug it in in a room in 1 outlet Turn off breakers while music is playing, when you hear the music stop, that breaker is powering that outlet. Label it. Now go back upstairs to that room and plug it into each outlet in the room until it either 1) turns back on, or 2) you're out of outlets. Label the outlets as to what breaker they go to. Repeat for all rooms/outlets in the house. The home-owner will probably thank you for labeling their breaker box.
Household power is normally 15A or 20A service per room, depending. So you can't power much from each outlet, you'll still need to run distro, but so long as you're below 20A of power you can use 12/3 cord--- also known as extension cords. 14/3 can get you buy up to about 15A. The cord size should be listed on the cord.
Also remember, HMIs and Kinos don't normally dim. There are some which do dim, but the dimming will be done on the ballast of the unit. Do not run it through a dimmer-board or hand-dimmer.
If you want to go all tungsten, you'll loose a lot of efficiency first correcting the tungsten to blue (2 stop loss) and then back to orange (2/3 stop loss).