Forgive me for resurrecting an old topic. I just had this happen on a z800. It made the click-beep-click-beep noise as described here just as soon as the power cord was plugged in. The system had been sitting powered down and unused for a while. This happened immediately on the first attempt to power it up. This system has the 1110W power supply, but it's possible the same applies to the 850W PSU. Here's what I found. After reading this forum topic, I decided to look inside the PSU. What I found was that two of the electrolytic capacitors on the circuit board were swollen at the top. This is a common failure mode for electrolytic capacitors. You can find any number of topics on the web, and videos on YouTube about capacitor replacement. That's what I did. I replaced the two caps, and now it works. In this PSU, the two caps in question are on the 5V supply. They are also the highest value and lowest voltage rating in the supply. The originals are 3300uF, 10V caps. I replaced them with 3300uF, 25V caps. It was after I replaced them and figured out how to energize the outputs with the PSU board out of its case that I found out these were in the 5V section. The system booted normally after being reassembled. The system has been cranking away at 100% CPU for the better part of two days now. The parts cost for the repair was < $5.00.
Note that when the PSU is removed from the z800 chassis and plugged in, the LED at the power cord end may still light up green as a health indicator. This is under no load. When a PSU with this problem is in the system, it is under load. What the symptoms sound like is a protection circuit kicking in and disabling the power output with a relay. That's the clicking sound. The beep was coming from the main chassis speaker. The protection circuitry was cycling, resulting in the click-beep-click-beep sound even after the power cord was removed, for a few seconds. I suspect there was noise on the 5V output that triggered the protection circuit because the two caps weren't doing their job of filtering the output.
*Disclaimer* I would never advise anyone to do this to a system under warranty, or with a service contract in force. I would never advise someone to do this who isn't very comfortable working on live circuitry, or using a soldering iron to do rework. All power was disconnected during soldering. Power was applied to the bare circuit board only for testing.