Coca Cola Koolatron soda can fridge blinking, not starting up

SPECS

Model Name - KWC-4C AZ

UPC - 059586510137

ASIN - B08SMQCNGX

Model Number - KWC-4C AZ UK

Brand Name - Koolatron

Refrigerant - R290 or R600a

Cooling Method - Thermoelectric

Power Plug - Type A - 2 pin (North American)

Lock Type - Electronic

Defrost System Type - Manual

Voltage - 12 Volts (DC)

Inverter Type - No Inverter

Compressor Type - solid-state compressor

Item Weight - 1.84 Kilograms

Item Dimensions - 25.4D x 17.8W x 25.4H Centimetres

Annual Energy Consumption - 235 Kilowatt Hours

A few years ago, I got my roommate this little desktop fridge to put his drinks in. After a few months, it stopped working.

When switched on, the light will blink once around every second, at the same time the fan attempts to start turning but only 'flinches' lightly. Every time it 'blinks', there's also a very tiny and soft 'zz' noise.

I've opened the fridge up, and the sound seems to be coming from the motherboard somewhere but I can't tell where exactly, or what the exact problem is. It was a bit dusty inside, but nothing really out of the ordinary and even after air dusting it, it behaves the same way.

I do see some bits that look kind of rough. The soldering job in some places looks like something I would do (weird and messy).

Any idea what I should look for or do to fix it?

EDIT: I don't know why I didn't think to do this before, but I did find my voltage tester, and found that the blue wire coming from the AC power socket does not seem to be emitting any power. Since I'm very new to this, I admittedly don't really know that much...

The question is now how should I go about fixing this, assuming this wire is the problem? I have pretty limited tools. I don't think I even have a de-soldering tool.

IMAGES

Note: Since there was no entry on this device, I made a stub. I've never made an article for a device before, though.