I did some research on pentax forums and found there's a huge thread about other modern cameras that have the same symptoms. Apparently it can be repaired and there's someone in NorCal who fixes cameras with this problem (aperture block failure) as a side-business, it has to do with a solenoid. Not many K-S1 cameras reported with the problem, but then how many people who bought them are going to try to figure it out? I was more or less planning on junking the camera because I thought it had a bigger problem initially. But now? I think I'll send it to the guy in NorCal, his price is better than the $300+ I would be charged to send it in to the official Pentax repair facility.
Since I already bought a solar filter, I figure I'll try it out. And while looking around for some manual lenses to use to try out the solar filter on the K-S1, I ran across my old K100, which I haven't used in several years and had forgotten about. But that led me on a search for my rechargeable batteries and is getting me to organize my stuff. I finally bought a cabinet for at least some of my stuff, and it would be nice to get it better organized. Right now things are wherever they happened to have landed last time I either used and now I wonder what do I really have (anything lost or forgotten about?), since I had forgotten all about the K100!
As far as practice with the solar filter, I'm now a bit torn about which camera to use - the K100 doesn't have live view, so lining it up with the sun is hit-or-miss (use a wider lens?) but I suspect that even using live view things could be hit-or-miss when it comes to guessing where to point the camera.
I bought the filter from B&H and they threw in some solar glasses. I'm not entirely sure I want to spend the short time available figuring out photo gear, I think I just want to experience it without stress. Of course, then I'll be envious of anyone who posts any awesome photos they take, if I didn't try at all.
Any more suggestions/experience with solar photography?