MPU6050 - GY 521 with Arduino Nano stuck at "Initializing I2C devices..."

I can't make MPU6050 work. I use NANO

I used this tutorial -

I can't pass Initializing phase.

There was and I2C scanner program (MPU6050 - GY 521 with Arduino UNO R3 stuck at "Initializing I2C devices..." - Sensors - Arduino Forum) but it also stucks on scanning.

As the guy from mentioned post, I connected VCC to 5V in Nano, but based on the comments that shouldn't destroy chip.

Some topics suggest adding pull up resistors to SDA and SCL - but the original article doesn't mention it.

How can I check if the chip is functional?
How to investigate why it doesn't work?

Could anybody help here?