I concur. First thing I'd try would be a different PSU, or at least making sure everything is plugged in properly and then a different PSU.

In the meantime, and assuming you have another desktop PC to hand, you could plug the hard disk into another PC and copy important files off it.

After that, the next thing to do is set up some backup routine that backs up important files to somewhere else every night or every day. One of the cloud storage services perhaps. Or, if you have more data, a combination of cloud storage and local network storage with a nice little NAS box.