Problem: If there were applications running on my ThinkPad T60p whose RAM usage exceeded, say, 350MB and I then tried to hibernate the system, I would receive the following error message from Windows:
Insufficient System Resources Exist to Complete the API
Only after closing the memory-intensive programs (Firefox, VMWare, Photoshop) could I then hibernate the system.
Solution: This Microsoft Knowledge Base article addresses the problem directly. There is a hotfix available for this bug, but you must phone a Microsoft support representative in person in order to receive it because the hotfix has not been fully tested and will only be made available to individuals that Microsoft has manually screened and determined are eligible for the hotfix.
The support phone numbers for the Windows XP Professional product are available here on the Microsoft website. If you are using a different variant of Windows XP, you should consult this page instead and click on the link for the version of Windows XP that you are running.
Microsoft recommends that you backup your entire system before applying this unsupported hotfix, and the ThinkPad Rescue and Recovery backup utility makes doing so easy. I managed to backup my entire system on two DVD-ROMs (after creating a recovery startup disk on a single CD-ROM).
After applying this hotfix, I was able to hibernate the shit out of my shit, and everything has been totally balls-out rad since.