The only thing I can think of is if there is a random short-circuit on the 12V rail somewhere. Difficult to fault analyse though. As replacement PSU will have their own harness to the mobo/component plugs, it has to be downstream of there, so could be HDD, optical drive, mobo. I would start by powering up without the first two and see what happens.
Amazon Fire HD 8 review: A brilliant combination of function and value – with one massive caveat