Help on incubator

I made an incubator system, but when I try to test it doesn't work. I used arduino UNO as controller, lamp, fan, DHT22 and DS18B20 and 16x2 I2C LCD. When I tested the system with a PC, the system was working fine. I think this is from my power source, as I used an external AC / DC 12VDC power supply to power arduino and from arduino I took the 5V to power all the different components (DHT22, and DS18B20 and 16x2 I2C LCD, buttons). My question is the system can work or not with the 5V of the arduino? Thank you.

If you have a phone charger using USB output, try that instead.

What is controlling the lamp? A relay? It would help us to help you if you post a schematic. Here is a tutorial on making a schematic that you can post.

Be careful when using the power plug or Vin. Powering through Vin or the power jack means that the Arduino and all peripherals that are on the 5V rail are powered by the onboard 5V regulator. With a 12V input the regulator must dissipate the extra 7V times the current. The on board 5V regulator is not heat sinked so will supply limited current before it overheats and shuts down. I would use a buck converter to drop the 12V to 5V or an old 5V phone charger and connect that to the 5V on the Arduino, bypassing the, weak, 5V regulator. Then the rated current of the DC DC converter is available on the 5V line.