Hi Helvetico, I shall try to answer your question regarding the problems which may arise with the boards.
I only have experience with two types of product, the SMART boards, and the Promethean boards. I currently work with Promethean boards and will give you my answers based on those.
There are basically three main parts to the system. The board, a projector and a computer. Promethean supply software for use with the boards, and this software allows the user to create interactive displays for use in a lesson.
In five years of use, I have yet to have an actual board fail. The worst I have seen is when it has been turned off or not detected by the computer, or someone has managed to un-calibrate it so the pen seems to react with the board several inches from where it actually is. These issues are usually fixable in minutes by someone who has a decent amount of common sense and some basic training on the product. However, even if the board failed totally, all that would happen is that the user would not be able to interact directly with the board. The display would still show, and the software would still run. Depending on how complicated you had made your presentation, and how interactive you had made it, it may still be possible to run the entire show from the computer.
Next up is the projector. Biggest issue here is the failure of the bulb. Obviously, once the bulb goes, you are back to text books and the chalkboard till it is replaced. Older style projectors will be ceiling mounted, and assuming someone on site is capable of replacing the bulb, and you have one in stock, it is about a 15 minute job to sort out. However, some of the more modern systems have the projectors fitted to the top of the boards in a "short throw" set up, and these bulbs can be easily replaced in minutes. Some really modern projectors now have LED projection, and these are supposed to last for considerably longer.
Finally, there is the computer side of it. In your case you would have to rely on whatever you currently do for tech support. None of the boards I have ever worked with would run without a pc, but I do not know if newer boards can be self contained. Promethean allow the software to be used by staff on personal devices, so you can create shows at home and bring them in on a usb device or by email.
So, if you had a system similar to the ones I use fitted, I would expect that you would take out some from of warranty and service deal with whomever you use to supply them. Depending on cost, you would get different levels of response time, ranging from a few hours to several days. It is quite usual to go for a "next working day" contract for devices such as this.
I guess this boils down to the projector being the most likely device to stop you from delivering your lesson. Apart from bulbs failing, I have had to replace several projectors over the years. In your position, unless still under warranty or contract, this would involve sourcing a suitable replacement and having it fitted. I would guess about a week to sort out. Note, the projector would need to be able to output the same size display at the same distance as the original, otherwise you would need to relocate all the mounts and cabling to the correct distance.

Finally, as we always used to say to our lecturers that complained when the network went down in my old job, "I trust you have a backup lesson ready and waiting to be used!"
I hope some of that makes sense, if you need anything clarified, please ask.