If I understand the translation, you have either: (a) a system that is idling down and entering the S3 low power state or (b) a system that is shut down (in S5 power state) but has Magic Packet wakeup enabled. Regardless of which, when a magic packet is actually received from another system, the system starts to awaken but fails to do so completely. Is this correct?
My first question will always be: Have you verified that the latest BIOS and the latest drivers have been installed for the motherboard and all add-in cards?
For the S3 case, this is often a driver issue - one of the drivers is not restoring its hardware state correctly. The most common culprit is the video card. Some BIOSs have a capability for reinitializing the video hardware during a S3 restore. If you have this capability in your BIOS, try enabling it and see if this fixes the problem...
...Scott