With the cheaper alternatives for solar cells, what would be the current ballpark cost to cover the roof of an average-sized house entirely with solar cells?
The "Rain-Man" answer is $30K without air conditioning and $60K with A/C. But you don't want to rely on those numbers because they don't apply to your particular situation.
Federal tax credits can reduce this cost by as much as 30% and state credits can knock off another 30-40%. It depends on the total system costs and on how the systems are installed (all at once or over several years). Then there's the issue of your payback-- it's fairly quick at 25 cents/KWHr (less than two decades) but a lot longer at eight cents/KWHr.
Another issue is how much of a system you need. It's always cheaper to reduce your consumption than to build a bigger system. Ask your local utility about a whole-house energy audit before you start pricing photovoltaics. Consider investing in solar water heating, energy-efficient insulation/windows, house-shading landscaping, and EnergyStar appliances before you buy a panel.
Again the Rain-Man answer is that installation has usually been about 50% of the total cost, but you're asking the wrong questions. You want to know about the total price and the quality of the installation & materials. Make your comparisons on the basis of the equipment and the durability of the techniques, not on the price of the installation. There are many cheap/fast installation techniques that will "save" on the costs, but will also come off your roof over the next 10 years (or at the first hurricane/snowfall). If a contractor is selling his cheap installation, then you don't want to use that contractor. You want the guy who's invested in advanced training, techniques, and tools... one who will also warranty his labor & materials for a long time, and be around to honor the warranty.
Right now it is 94 degrees outside and ~ 87 degrees inside. I live in a 3rd/4th floor condominium converted from a house. I'm wondering how much cooler it would be if all of the sunlight beating down on the roof was not there (ie hitting solar panels). While it might not make sense if I was using it just for the electricity, the question is could it significantly cool down the house?
I don't think it makes much of a difference, at least not on our house. South-facing roofs are the hottest parts of the house to begin with, so cooling them 10-20 degrees won't make much difference in the heat transmitted through the roofing materials. We saw that reflective foil roof insulation and good wall insulation will make a much bigger difference than the blocking effect of the PV panels.
Does it matter if I have a slate roof?
Holy cow, I'll say it matters.
First, any sunlight hitting the slate is very efficiently transformed into heat and transmitted to all other parts of the roof. So covering half of your roof with PV panels might reduce the solar impact on the slate but it'll just allow the remaining exposed slate to transfer its sunlight heating to the other half that much more quickly. Net effect won't be noticeable. You'll only keep the heat from coming into your attic by installing radiant foil roof insulation and good wall/attic-rafter insulation.
Second, slate roofs are expected to last 75-100 years. Have it thoroughly inspected/repaired by a slate-roof expert before you let any solar installers up there. Make sure the slate guy knows what you're planning so that he can make the appropriate recommendations & repairs. Then invite him back after the solar job is done to check that no new problems have been created.
Third, I suspect you'll have a terrible time finding a solar contractor who knows how to handle a slate roof-- let alone one who has the proper tools & roof racks. Their profit margins depend on speed & efficiency, and they're optimized for composition shingle roofs. You're looking at high-end custom racks with special mounts and painstaking installations, plus scaffolding and additional safety gear to move around up there. I doubt that they would want to drill through the slate tiles, which means that they'd have to remove some of them or build around/over them. I'm sure that they could eventually figure out what they need to do, but it'll be expensive.
An option for a slate roof might be photovoltaic roof tiles, not PV panels. This would involve removing slates (or clipping/gluing the PV tiles on top of them) and not using racks at all. However the PV tiles aren't used very much and are at least 2x-3x the price of PV panels. Again it's a lot of finicky work.
The best long-term option might be to ditch the slate roof and start over. You could build the new roof the "right" way, with insulated/reflective foil/foam panels under the sheathing, and add in the mounts for the PV roof racks as you're putting the roof together. While you have the roof off you might get more access to the walls for adding insulation (if necessary) to minimize heat intrusion. You could also route conduits for ceiling fans and photovoltaic cables instead of having to mount them externally to the ceiling/roof. The new roof would have ridge vents or solar-powered attic-exhaust fans to keep the voids cooler and reduce heat transmission to the house ceilings. You could use reflective shingles to drastically reduce the heating effect in your house, which should cut way back on cooling costs. Or you could go aluminum with integrated PV panels. But while the result would be elegantly integrated and aesthetically pleasing, it might not meet neighborhood style codes and could be horribly expensive. In this case, though, the "expense" would be in the up-front costs of doing it right instead of in the years of dealing with all the compromises of mounting PV racks on a slate roof.