I bought a ZE4430 back in August and I believe we have the same problem. The noise only happened for me on battery power and was very hard to predict. It was very annoying too... it sounded like there was a cricket stuck under the keyboard! It seems to affect all Athlon based Pavilion 4xxx series all the way back to the 4100 series!
If you go over to the IT Forums HP's website, there are various theories as to why this happens. The best explanation I found deals with a capacitor improperly using a throttling frequency of 2khz. This throttling takes place when the mobile Athlon dynamically switches speed based on CPU load. Anyway, 2 khz is in the range of audible sound, hence the noise. Try this thread to see what I mean:
http://forums1.itrc.hp.com/service/forums/questionanswer.do?threadId=67056
This sounded a little too Star Trek to me as well at first, but several people claimed that a BIOS update should fix the problem by pushing the throttling frequency beyond the range of human hearing to 30khz. Sure enough, BIOS revision KA.M1.49 squashed the cricket! It's not really posted anywhere I could easily find on the HP site so I had to do a search for it. You can find it at:
http://h18007.www1.hp.com/support/files/hpcpqnk/us/download/19390.html
It's a self extracting executable so it should do all the work for you, update the BIOS and reboot the machine. Just make sure you don't have any antivirus software running since it gets tripped up in it.
If you're nervous about flashing your BIOS without further proof that we have the same problem, try this. Download this CPU control utility (which is nice to have even without this problem!):
http://www.diefer.de/speedswitchxp/index.html
Load it up and set it to Max Battery. If the noise goes away, then we have the same problem and you can safely do the BIOS update. Of course the catch here is that this utility only seemed to have any effect for me only after I updated to BIOS revision KA.M1.48 which is also available on HP's site. Just go and search their drivers section for the ZE4430 model. So all in all, since you probably have to do a BIOS update to see if we have the same problem, you're probably better off flashing to version 49!
Whatever you do, don't involve HP! They're clueless. They thought it was the hard drive, then the battery, then the CPU fan. What nonsense! I even sent it to them to get it repaired and they sent it back with the same problem and with a scratched case to boot!
This is somewhat long winded, but I hope it helps!