So, I fixed this problem by downloading the compatibility library on another computer connected to another network (same as before, via the right-click menu in Eclipse), and then copied the resulting android-support-v4.jar support to the source computer .
The new file was about 137k compared to the 104k version that my local version of Eclipse received. I'm not sure where the discrepancy comes from, but I think that my blocked corporate Internet access blocked the selection of files from the library and left me with an incomplete version.
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