I know its been months but I'd like to post a similar situation. I've got 2 PXI-1044 chassis and the primary one failed. With the power button pressed in the chassis would just make a slight clicking sound, the fans would not spin and the power button would lightly illuminate in sync with the clicking sound. I pulled the Power supply shuttle and threw in our spare PSU. And it worked for a week but then the spare PSU shuttle began having the same failure! clicking and no power. I went to check on the defective primary PSU and now it was fully functional!
Tech support offered nothing more than check the voltage on the rear voltage monitor connector. Its 0v, they're all 0v. Its a failed PSU.
I've used this chassis on other testers and they run non stop for several years, unusual to have this problem on two chassis for the same tester.
I am going through the RMA process for repair right now. $2k and hopefully NI doesn't tell me everything is functional