Weird, I checked make xconfig in my kernel source and it said skge is the module for this card
(my netcard use this module as well, mine is onboard Marvell Technology)
You can see module suggested in lspci with -k option
Now if you want to test with R8169 module, try:
unload skge module if it is loaded (check /sbin/lsmod)
But modprobe it should have been handled by udev at boot...
Maybe there is conflict with skge module, blacklist it could help
echo "skge" >> /etc/modprobe.d/blacklist.conf