What does Device Manager say about "My Computer"? If it says "Advanced Configuration and Power Interface (ACPI) PC" or some such -- depending upon the particular system -- then you should be able to standby / hibernate, assuming that none of your devices and / or software are interfering in some way. If the computer is designated as a "Standard PC", then a Hardware Abstraction Layer that doesn't support the feature was installed. Other possibility would be that many server configurations don't support standby and hibernation for fairly obvious reasons.
Hope you get it sorted.
Regards,
Jim