Currently, the Realtek R8168 driver does not work in a 2.6.24 kernel because of changes in the kernel structures. I found a patch on the Ubuntu Forums which adjusts the driver source so it can compile for a 2.6.24 kernel. The patch was written for 8.005.00, but I verified it working for 8.006.00 (latest version at time of writing). The patch is attached.
Download driver here.
Got the patch from here, but for your convenience, I've attached it to this article too.
Note that these instructions are also found on the page at Ubuntu Forums
After unpacking the driver, copy the patch in ./r8168-8.006.00/src/. Then run:
cd ./r8168-8.006.00/src/patch < r8168-8.005.00.hardy.diff.txt
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