Well, Gary's hit most all the important stuff, so I'll just add a bit.
My experiences with my '81 XS is that its carbs are very sensitive to sitting for extended periods. The most common symptom was it would not start. Almost every time I've let the bike sit for more than a few months, I've had to pull the carbs and thoroughly clean them. I'm almost positive this is your problem.
One thing Gary touched on, and I'll just add to it a bit based on my own experiences: when you go to remove the carbs, there's a procedure, I've found. First, I remove the airbox and filters. Next I remove the cam chain adjuster cover. It's a lot easier getting the carbs off when it's out of the way. Then I remove the carbs from the intake boots. Supposedly, they can be removed at this point -- from the right side is easiest. But it's even easier if I also remove the right side intake boot. I usually don't have to remove both. Even so, it's a close fit, and you might have to maneuver the carbs around some before they'll come out.
+1 on Gary's recommendation for using an impact driver. When dismantling the carbs you will most likely need it. If a screw is really tight, don't force it with a screwdriver, cuz you'll probably strip it. Use the impact driver instead.
Sometimes it's better to dismantle the carbs one at a time so you'll have a reference for putting it back together. Or you can take pics with a digicam as you disassemble. To inspect/replace the needle and seat and/or clean out its orifice, you'll need a drift punch to remove the pin that holds the floats in place. As I recall, this pin is knurled on one end, so you want to drift out the pin from the other end, such that the knurling does not have to pass through the post that holds the pin. Do NOT lose that tiny clip that holds the needle to the floats. My experience with this needle is, because it is rubber tipped, it seldom goes bad, but it's a good idea to clean the seat and orifice anyway.
Do you have access to an air compressor? I have found that spray carb cleaner, which does an excellent job of cleaning the carbs, does not have sufficient pressure to properly clean or clear the carb's orifices. I use an air gun with a small nozzle for this. BTW, just in case you don't already know this, it bears mentioning: when spraying the carb cleaner, wear gloves and eye protection. That stuff passes right through the skin via osmosis and is bad for your liver.
As for the no-start condition. My '81 had a similar problem. Good starter and fresh battery, but most of the time, it would not start. There are two relays, as I recall, that control the starter's operation. I'm not exactly clear anymore as to exactly what each one does, but I know that one involves cutting the headlight circuit in and out. I dismantled both and cleaned the points contacts because they were pretty heavily oxidized, and thoroughly cleaned all the connections. That took care of the problem.
You mentioned the coils. One of the inherent problems with the XS and old, weak coils is, when you try to use the electric foot, the starter is pulling so much juice from the battery that there isn't enough left for the coils to generate a sufficiently hot spark. Result is the bike is reluctant to start with the electric foot, but will usually start on the 1st or 2nd kick. My bike's like this -- still has the original coils.
There is a recent thread here -- by INXS -- that discusses the starter system on the XS at length. You should read through this. If one of the seals has gone bad, your starter might have filled up with oil and crud and not be working efficiently, thus drawing even more amps from the bike's puny 14ah battery. If you decide to remove the starter, be sure to drain the oil first, or you'll have a mess on your hands.
That's about all that I can think of for now.