There is no cure from Microsoft about this issue. The end user would have to free up resources. Usually this begins with a primer about resources.
The Memory article under Optimizing Windows at http://www.aumha.org/articles.htm shows us that these resource pools are 64 thousand byte non-expandable spaces. No matter how much memory you add, the resource pool is still 64 thousand bytes.
And again, Microsoft will not be issuing a fix for this.
------------
Given this, you have to find what is eating the resources and eject or uninstall it. Nothing in your post gives a clue to what is consuming the resources so in this post all I can offer is what resources are and note the above site about optimizing.
A common issue with such machines is they boot up and run many applications as it starts. The STARTER program I note at http://reviews.cnet.com/5208-6132-0.html?forumID=32&threadID=1313&start=0 has a link to such.
At the same link is the Anti-Parasite Suite that eject other pests that today's antivirus ignores.
Bob
Dell Dimension 4100, 20 GB/Windows ME/Noton Anti-virus/IE 6. AOL broadband.
I was getting the message: resources are extremely low while working with a floppy; the machine would freeze. I deleted all files I considered not relevant. I had adobe 4 & 5 installed. Uninstalled both and downloaded adobe 6. When I restarted the machine I got this:Error staring Program. The MSIEXEC.EXE file is linked to missing Export MSI.DLL:22.
Any help put there?

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic