I agree with trying it outside the new case on cardboard or wood surface. Anything that doesn't conduct.
But it probably is just that the PSU died, and it was a coincidence that it happened when you added the SSD. Life is that way sometimes.
Although it could be there was an issue with it and that was the final straw. Regardless I'm guess that is the only issue.
Couple extra thoughts. Try it with a different power cord and different wall socket. Stranger things have happened.