98 LeSabre problem
 

I need some suggestions.My Mom has 98 LeSabre,about 150K miles,fairly good shape and very few problems over the years.
She called tonight and said that when she got where she was going,about 2 miles from home but far enough for the car to be warmed up,when she went to shut off the car it was making a banging noise from the front.So,I went down to see what was happening.Started the car,had been sitting about a half hour,no noise.So I drove it home.
When I got there,there was a thumping noise that I thought sounded like it was in the right front,possibly the right front wheel.Opened the hood and tracked the noise down to the radiator.Shut off the car and stopped the fans,to make sure it wasn't a bearing in the fans,noise continued.And I could feel the radiator thumping.Removed the cap,water sprays out,I expected that.Let it cool down,refilled the radiator and started it with no cap.I squeezed the outlet hose on the other side of the radiator and it spurted water from the fill neck,so it seems there's flow between the tanks at least.When I knew it had run long enough to be warmed up,made sure it was full and watched.The water in the radiator never moved.No surging,no flow,nothing.
I'm wondering if it's telling me that the water pump is shot because if it's working,the water should move.
Any opinions?
Thanks.