Error: Insufficient system resources exist to complete the API.
This message ("Insufficient resources exist to complete the API", along with an event log event ID 26 from "Application Popup") has been popping up on my laptop from time to time, along with the rather troublesome issue that the machine refuses to hibernate. I had it set up so that I could close the lid, and the laptop would stand by for a few minutes, then hibernate.
Suddenly, it seems, the laptop is unable to hibernate, and only this confusing message appears on the screen.
Realisation dawned this morning that I had recently installed an extra 512MB of memory into my laptop.
Of course there are no system resources for hibernating, because my hiberfil.sys space is 512MB smaller, having been created with the previous size of memory.
The solution is simple - open the power properties (right-click the battery / power icon in the notification area, and select "Adjust Power Properties"), click the Hibernate tab, and then uncheck the "Enable Hibernation" box.
Click "Apply", to delete hiberfil.sys, then re-check the "Enable Hibernation" box, and click "Apply" or "OK" to recreate it.
So, if your computer cannot hibernate, and you get this message, try disabling and re-enabling the Hibernation feature, and don't think it's as random-sounding a process as other articles make it out to be. If you've changed your memory size, you need to change your hibernation file's size.
Just in case this doesn't fix you right up, there is another issue that it might be - a hotfix is available for Windows XP SP2, XP Tablet Edition 2005, or XP Media Center Edition 2005; there's also an earlier hotfix for Windows XP, for a different issue on multi-proc machines.