Air carrier Captain reported an autopilot problem and returned to departure airport.

Narrative

Climbing out; hand flying. Passing 10;000 feet; went to engage autopilot and it would not engage. Tried multiple times including after shutting off both AFS (Autoflight System) switches individually. We were scheduled to ZZZZ; so this made us non-Rasmussen capable. After talking with operations and maintenance to try to sort out our problem; the determination was made to return to ZZZ. This meant we had to dump fuel to get below max landing weight. We were approximately 40 miles WNW of ZZZ1. We communicated our plans to Center and coordinated the fuel dump. We were at FL280 when we started our dump. We dumped approximately 70k in fuel and made a non eventful landing in ZZZ. No emergency was declared.We had a 'no autoland' CAT 1 alert on taxi out. We performed a PDM after coordinating with operations and maintenance. During that time and discussion; we also noted our autopilot box was amber. We asked if it would work or was it associated with the no autoland. There was no way for them to confirm. A note in the MEL associated with the no autoland about checking the AP box status might have helped guide us to the gate for maintenance action.