Finally we opened the manual and looked at the exploded drawing. There was a picture of an O-ring (Part 41) on the magazine tube. I looked at the gun. No O-ring.* I opened up the box containing shims and choke tubes and the like and there was the missing ring. I put it on the gun per the manual and the gun cycled perfectly after that.
Manuals for almost any gun can be found in printable versions online, and manufacturers will usually send you one free of charge for any current or discontinued model. Get your gun's manual and keep it handy. It may not be the manly thing to do, but it's the smart thing.
*O-rings get a bad rap. Remington reps tell me the metal rings on an 1100 are more likely to break than the O-rings are. Replacing them with sturdier hardware store O-rings only keeps the gun from fully closing into battery.