I decided to solve this the expensive way. This is a new router, so I assumed it was working correctly. But there have been some other funny things going on in the network, including sporadic inability to get the the Interent even though the cable modem looked like it was working.
So I got a new router, this one with gigabit switch ports. I do a lot of file transfers between a few of my computers, so I decided to get a gigabit LAN card for one of them and plug it into a gig port in the router and plug the iMac into one of the gig ports.
I manually configured the iMac to gig speed and that's what shows now in Network Utility. So my guess is that the other router had a bad port. I didn't switch the cable to another port to see if it was a true 100 mbs, but I think I'm right.
All's well that ends well. I appreciate you pointing me to the place where I could do the manual config. I'm pretty good with PCs but this is my first Mac and I don't always know where to go to do things.
Mike