What forensic analysis techniques target computer components other than the hard drive once the device is powered off?
If it's soon after the device is powered off, there are attacks that may allow to recover RAM content, e.g. Cold Boot Attack on Wikipedia, Memory forensic data recovery utilising RAM cooling methods.
There are also some secondary things that come to mind e.g. serial numbers might be used to trace where and when (and thus by whom) parts were purchased; and there might be a firmware trace showing when the system was last used (which may be important evidence in certain cases) but that feels a very niche use case.