2001 Ford F-150 Starter solenoid not engaging?

My F-150 will not crank. I thought it may have been the battery, so installed a brand battery, still just makes a single click when you turn the key, and nothing engages or turns. When you turn the key and it makes the click, the lights on the dash go dim or go out. I am thinking it may be the starter solenoid? This truck has had some electrical issues in the past, sometimes the odometer just goes blank and comes back on again. Any help appreciated.

Dan