The 300w not turning on is something I'm not too surprised with.

I don't know what card you're running in there but 300 watts is not enough for most current day gpus. Especially with a grey box 300watt psu.

If the card works flawlessly sometimes but most of the times not and the psu is clicking... Then the cause from where I'm standing is clear: there is a short. In the psu, the card or the cabling.

I see a lot of cables/connectors right against the card. Are you sure there is nothing creating a short?

Does the box start without a gpu in it? (leds on, fan starts turning) If it also clicks in that config with both psu's.... Check the cabling.

Does the card work flawlessly in another system?

Solution 1: get another hefty psu like the 750w which normally is in that box. Check with that.

Solution 2: check for shorts, all cables clear and not damaged? no marks, no connectors against a piece of metal? No weird marks on the card?

Solution 3: send it back and get it replaced. If it looks faulty it probably is.