We were able to connect the battery to the PowerBoost, the Powerboost to the 3.3V regulator, and power the PIC from the regulator.  We also managed to connect the output from the battery to the PIC’s ADC so we can measure the battery level.  Currently we are showing the battery level on the LCD screen for testing purposes.  The output compare module was configured to generate the pwm signal for the servo control.  However, when connecting the motor control wire to the PIC output compare pin it causes the LCD to stop working and the PIC needs to be restarted.  After some more testing we also found we could no longer program or power our PIC over USB and it would only run on battery power.