What does position 1 on the switch on the back of your case mean - power is being supplied by your PSU to the motherboard? You are more likely to have the motherboard coin cell go flat sooner if power is removed from the motherboard altogether when not in use so the above should be the case for battery preservation (although I suspect it'll cost you much more than a new coin cell in terms of wasted power over time).
If you have a disk in the DVD drive then empty it until you actually need it to use it - that's the simplest way to cure this problem. I suspect that an external connection may be attempting to wake the PC from its fully powered off state. If it is fully powered off, it won't be any of the software you mentioned responsible because they won't be running on a fully powered off PC. Does the PC behave the same if all external connections such as LAN, any modem or other non-essential peripherals are removed/unplugged? You could try disabling wake on LAN in the BIOS settings and Wake on Ring or Wake events for whatever your modem is connected to (if you even have one on this PC).
My reference to '1' regarded the PSU switch: I can either have it set to '0' or '1'.
There is no disk in the CD/DVD drive. There is no modem in the PC.
I removed the RJ45 cable from the network interface to completely disconnect the PC from the router to see if the noise continues. The noise does not occur very often so I will have to live with it for a day or two to know if this modification changed anything.