I appreciate all of the comments and suggestions. TruCelt, that talcum idea is brilliant! I think I will try that.
I also talked with the roofer again, and he suggested hanging out in the attic while it’s raining and seeing if I can find the spot where it’s coming in, and also getting on the roof and putting some caulk around a couple of vents that are on the roof right above the kitchen, where the water is. Hopefully that is where the water is coming in, but I think I’ll use that talcum idea just in case it isn’t. I’ve also never been in the attic before, so I don’t know if there are pipes, cables, etc. I’ll check those.
phreesh, I am a bit hesitant about getting into the attic, as well as going on the roof, but only because I have a slight fear of falling off of ladders. Not necessarily of heights, just that I’ll fall off of the ladder when I’m climbing onto or off of the roof, or climbing into or out of the attic (there is just a little opening in my garage by the ceiling). Yes, I know how crazy that sounds, and yes I wish I could get over it…
A lot of good advice here, especially the baby powder one. One thing that I didn’t see mentioned is that if you are going to go into the attic and start stirring around the insulation, it would be a good idea to wear a dust mask even if it’s only a bandanna.