Arduino Pro Mini not doing anything when powered independently

I have a small circuit setup consisting of Arduino Pro Mini with a modified I2C MPU6050_DMP6 code, running on 3.3V 8MHz mode with 19200 baud , MPU6050 gyroscope, 1.5V-3V vibration motor and CR2032 3V coin cell battery, and an Arduino UNO with the ATMega chip removed from the board to upload the code to the Pro Mini.

When I connect the Pro Mini through the Arduino UNO to the PC, it operates normally as programmed, (i.e vibration motor & on-board LED turns on when the gyro is on a certain angle etc.), but when I run the circuit independently on the 3V battery, all components are on, but do not function at all.
And do note, when connected to the Arduino UNO, the voltage supply from the Arduino UNO is 3.3V, so the voltage difference from the UNO and coin battery is only 0.3V.

Is a CR2032 battery sufficient to power the Pro Mini and MPU6050?

Is a CR2032 battery sufficient to power the Pro Mini and MPU6050?

Probably not, especially considering the motor and LEDs as well. The peak current draw for CR2032 cells is usually considered to be 15 mA.

Try powering the setup with 2xAA batteries.