Well the RTL8139 module doesn't work with RHEL5 (as it's specified to be compatible...).
#1 Go here
and download the proper driver named 'LINUX driver for kernel 2.6.X and 2.4.X (Support x86 and x64)'
#2 Do :
Go to the folder where the file has been downloaded, then :
#tar -xvf r8101-1.016.00.tar.bz2
Now go to the folder where the files have been extracted and :
#make clean modules
(or r8101.o for kernel 2.4.x)
After the reboot, the server should be correctly connected (consider that the parameters are ok -eg. DHCP or IP address).
If not, type :
#/sbin/services network restart
That's it... Just keep me up about it plz.