3,6V DC motor spinning with L298N and Arduino
The L239 is a terrible motor driver. It's the kind of motor driver Noah used to control The Ark.

It requires a power supply that is at least 2.5V more than the "logic input high" voltage, which is rated at 2.3V. That means an absolute minimum of 4.8V, which is borderline for the Arduino's 5V pin, especially if you are running off USB (which can drop as low as 4.75V and still be within specification) and way out when powered from the battery.  It's really designed for driving motors in the 12V+ range.

To drive a low voltage motor like yours you need to pick a more modern MOSFET based motor driver.