Kristin,
R, and conversely GME, needs to read the entire problem into active memory. Because of this you have to account for the amount of RAM necessary to address the problem. This is particularly true for matrix type operations. For spatial modeling using R it is quite necessary to run a 64-bit OS with at least 6GB RAM. If that is the case I would look at your R installation. When you install R it, by default, installs both 32-bit and 64-bit versions of the software. There is a possibility that, if the 32-bit version is installed, that GME is pointing to it and not the 64-bit version. There may be a way to reconfigure GME to point to a specific R installation. Otherwise you could uninstall R and then when you reinstall customize your setup and unselect the 32-bit assembly.
Not to be critical of Hawth Beyer's fine work on GME but, I would encourage you to just learn R. There is, admittedly, a learning curve but there are also considerable online resources as well as several active communities that provide support. Because of what I imagine are programming necessities many of the tools in GME are not necessary to ideal way to accomplish a given task. The results returned from Distance Among Points can be accomplished in a single line of code in the spdep library. With spatial objects being standardized around the sp class, the addition of the raster library for out-of-memory processing, a port to the geos topology Java library via rgeos for vector overlay and a port to GDAL via rgdal for reading/writing spatial raster/vector formats R is a fairly comprehensive software for complex spatial analysis.
