Looking quickly through my Di2 manual. What battery did you have prior to installing the new BT-DN110? If it was one of the SM batteries (SM-BMR2 or SM-BTR2) you may have mismatched firmware versions. The SM batteries may have V 3.0 firmware, while the BT-DN110 comes with V 4.0.0 or later. According to the installation NOTE "If your version of E-TUBE PROJECT software and firmware for each component are not up to date there could be problems operating the bicycle. Check the versions and update them to the latest ones."
And, in the E-TUBE PROJECT manual, on page 1 there is this CAUTION: "After starting a connection check, never connect or disconnect the battery or units until the procedure is finished and the application has been exited. Failure to follow these instructions may cause the SM-PCE1 / SM-PCE02 / SM-BCR2 and the units to malfunction."
Finicky stuff, this Di2.