The subject says it all, this problem happens 75% of the time. I usually need to reboot the ipod a few times before it will play anything.
The high pitched noise starts immediately after boot-up, although sometimes it starts after a song or two has played. I can't find any pattern.
Resetting the settings does not help, with default settings the problem still happens.
I have this problem with release 3.0, the current build, and unsupported builds. 2.0 never had this problem.