Is my Windows PC power supply broken?

To answer this question, I went straight to the source, to Jerrold Foutz of Power Supply Design Tips and a generally superb chap. Here's his best shot at answering your question:

I don't answer questions about PC power supplies because as a power supply circuit designer I need a schematic and a meaningful parts list as a starting point. Schematics for PC's, and especially their power supplies, are almost impossible to come by (it is highly competitive and no one wants their competitor to have this information), and if you get one, the parts list is mostly proprietary part numbers and there is no way to find data on the part and learn its characteristics.

Having said that, here are a few observations, which may or may not be valid. Take them for what they are worth, partially informed opinion.

Circuit breakers are usually of the magnetic or thermal sensing type, with thermal sensors being the cheapest, hence that is what is probably used in your PC.

They are triggered by higher than normal current heating up a non-linear resistive element that at a certain temperature (related to current) will open the breaker. You have to add the ambient heat to the self heating, so the breaker may open sooner in a warm room, or when air flow is restricted, such loose papers blocking a vent, etc. They are also mechanical devices. This means they are often not as reliable as electronic components and they can be more subject to shock and vibration. A breaker about ready to open might be triggered if the computer is bumped. If your power supply is operating at its limit, a random bump could explain what is happening to you, as unlikely as it seems.

The thing that bothers me is that the opening of the breaker does not trigger the response to a non-controlled shutdown. If the computer is in a sleep mode, loss of power might not trigger it. However, I'm just guessing here.

If something goes wrong in either the computer start-up or shut-down sequence, the standard fix is to turn off the power, wait 30 seconds for internal capacitors to discharge and then turn it back on. This is probably one of the most controlled sequences your computer goes through and almost always works. It seems to be working in your case.

One exception can be the sleep mode. Here, there is a low power drain to keep some control circuits alive and this may interfere with recovery. In this case, the time honored fix is to remove the plug from the wall, wait the mandatory 30 seconds, plug it in, and then turn it on. For laptops, you have to remove the power cord and battery, wait 30 seconds, then put them back in.

If this does not work, you usually have to send the computer in to a qualified technician for the product for repair or replacement.

You may be able to get some help on forums that cater to the PC hobbiest, but it is the exception to get a good answer. My batting average is less than one hit in 25 tries.

Although it only contains a line or two related to your problem, you might want to read Notes on the Troubleshooting and Repair of Small Switchmode Power Supplies, which is one of the links at RepairFAQ.

I know this did not answer your question, but hopefully it gives you some insight into what may be happening.