>>the PC that we choose to act as a File Server ... two 80GB Seagate disks at 15k rpm setup with a SCSI
RAID-0 controller.
Firstly, no server should be running RAID 0. You have twice as much chance of losing your data through physical disk faults. If you can, change to RAID 1 - this mirrors data from disk to the other, so you will be half as likely to suffer data loss through physical disk faults as opposed to a single disk. Compared with your current setup, you will be 25% as likely to suffer data loss. If changing to RAID 1 is not an option, make sure you have regular, good full backups and test them occasionally.
Regarding the error:
1 - check your virtual memory settings. Control panel -> system -> advanced -> Performance -> advanced -> virtual memoey -> change. Set the virtual memory to be 1.5 times the amount of physical ram installed. Set this for both the initial and max size and click OK on all windows. Restart the machine.
2 - check this article from MS:
The computer occasionally does not hibernate and you receive an "Insufficient System Resources Exist to Complete the API" error message in Windows XP with Service Pack 2, in Windows XP Tablet PC Edition 2005, or in Windows XP Media Center Edition 200
Sounds like a problem with hibernation - check your power settings in control panel and make sure you have disabled automatic hibernation (set standby and hibernate to 'never')