While UEK4 kernel out-of-the-box after updates had wired networking (but not wireless - which I fixed - see here for details of that work), the poor unfortunate UEK3 kernel on Lenovo P70 Thinkpad had no networking at all ! Both wired and wireless were totally absent. However, I was able to get wired networking going on UEK3 thanks to steps from this post here.
First, download the drivers from here. Then unzip and untar the file. Now the steps remaining are really easy. Just do the following as root user and wired networking should work after reboot. Note, in your case you will have an different "/home/username" of course.
To do the required "make install" you will need kernel headers for the running UEK3 kernel.
To do that, boot into the UEK4 kernel which by now has both wired and wireless networking if you have followed my guides above for getting wireless working on UEK4, and then use the guide here to download the kernel headers needed for the below command, and then reboot back into the UEK3 kernel and install the required headers, using rpm -ivh kernel-headers-<kernel-version>. If you did the steps to get wireless working on UEK4 you will already have UEK4 headers on your machine, in which case yum will complain that headers are already installed and refuse to install the UEK3 headers. In that case just do a "yum remove <UEK4 headers>" and then you'll be able to install the UEK3 headers needed. After finishing, you can optionally remove the UEK3 headers and put the UEK4 headers back.
Now do do the below commands and then reboot to get wired internet on the UEK3 kernel on the P70 ThinkPad.
cd /home/gstanden/Downloads/PRO1000/LINUX/e1000e-3.3.4/src
make install
Now reboot into the same kernel and wired networking should be present.