So, I downloaded the latest driver from RealTek to attempt to solve my problem. I removed the old r8169 with rmmod, but when I do a "make clean modules" from within the directory with the Makefile, I get the following errors:

make -C src/ clean
make[1]: Entering directory `/root/temp/r8169-6.003.00/src'
rm -rf *.o *.ko *~ core* .dep* .*.d .*.cmd *.mod.c *.a *.s .*.flags .tmp_versions Module.symvers rset
make[1]: Leaving directory `/root/temp/r8169-6.003.00/src'
make -C src/ modules
make[1]: Entering directory `/root/temp/r8169-6.003.00/src'
make -C /lib/modules/2.6.18-1.2798.fc6/build SUBDIRS=/root/temp/r8169-6.003.00/src modules
make: Entering an unknown directory
make: Leaving an unknown directory
make[1]: Leaving directory `/root/temp/r8169-6.003.00/src'

Can anyone tell me what's going on? Do I have to have untarred the files into some specific directory?

[Update a few minutes later]

Well, this is kind of discouraging news:

Beware: --------

Asus M2A-VM
- ACPI issues, can be worked around
- sometimes would hang on boot whether acpi=off was passed or not
- Realtek RTL8111B PCI-E gig-E ethernet issues with even newest kernel, and/or r1000.c driver from Realtek.

Emphasis mine. Guess I need to stick in a different card, but when I tried that before, the installer didn't seem to recognize it, either. It would also be nice if there were some way to disable the on-board RealTek device, but I haven't seen anything in the boot menu.

[Saturday update]

It is possible to disable the RealTek device, and I've done it, but a Fedora install still breaks when encountering the card I put in to replace it--a Linksys LNE100TX.

I've used the Intel gig-E card with driver code downloaded from Intel's site. The code and the card never gave me any trouble.

It would also be nice if there were some way to disable the on-board RealTek device, but I haven't seen anything in the boot menu.

I have found that a well placed hammer strike generally fixes these types of problems.

"make -C src/ modules"

You have what might be an extraneous space after the slash. Try either getting rid of it, or symlinking " modules" to "modules" (if makefiles is too dense to figure out, or machine-generated and you don't want to try messing with it.)

I have found that a well placed hammer strike generally fixes these types of problems.

For some definition of "fix," yes.

This thread kinda sounds like your issue:

http://www.linuxquestions.org/questions/showthread.php?t=477107

Though I don't know if you will like the fix this person ultimately applied. It appeared his symlinks were fuxord.