Lawnboy electric starter (Honda160CC engine)

The electric starter does not function. I took it off and put power to it and it turned. I reinstalled it. Battery freshly charged. Turned key, I get power to the starter terminal but it doesn't even click as it normally does with a run-down battery. The mower starts easily with the pull cord. (I've been living with that for a couple of years but now I feel industrious)