You did the right thing : Just 4 connections (+5V to VCC, GND to GND, A4 to SDA, A5 to SCL).
After that the i2c_scanner should see the device.
Do you have another i2c device ?
Perhaps you should try that first, to see if the Arduino is working.
Use the i2c_scanner to test it.
If the i2c_scanner can't find anything, some connection is bad, or your sensor board has a problem.
Test everything very careful, and check the sensor board with a magnifying glass or take a picture with a camera with macro.
Check every solder point. Measure the 3.3V on the sensor board.