Well, I'm unsure as to whether it can affect SSDs the same way, but I've seen HDDs hang when using Molex to SATA adapters, or in general, bad SATA (power) connectors [native from PSU].
Also, as paperwastage said, try another SATA (data) cable as well.
If neither of those options work [changing the data cable or trying another PSU], then I'd move on to diagnosing the motherboard.