Pro/Engineer doesn't recognize network card

Get the program cpu_id from ptc.com and see what NIC address you get.

Is this computer a laptop with a WiFi card? Or does it have more tha one network adapter of any kind? Both of these will cause problems because the license manager will only see one of them. Run IPCONFIG /ALL again and look for more than one MAC address. Also, if the computer is not actually on the network (which for you is a cablemodem) the card still may not be recognized as existing at all. In other words if you have to run software of any kind to access the network make sure it is running and try again.
Good Luck!!! I had a similar problem and never ever got a working answer from PTC and gave up.

You don't want to install a license server. You need to choose "Nodelocked license" or something like that. The license server is a FlexLM deadly-bobber for one server serving licenses to many boxes on the network. You are using a node-locked license. Not the same thing at all. If I remember correctly there is a point early in the install routine which gives you the choice.
You now have to uninstall the entire thing. Pro/E won't reinstall to the same place and most likely if you try to just reinstall it but choose another license method, it'll still remember the first method you chose and not give you the choice. You want to get EVERYTHING when you uninstall it, so use the Winshit uninstaller. Then do a clean install and watch for the nodelocked choice. If you didn't get asked for the location of your license file then you did it wrong the first time. I *think* it was the last of three choices you get in one of the windows during installation.
It's true that having more than one NIC will confuse the licensing system. If you turn off the *second* NIC during the install (you can do that from the NIC-management folder in control panel, just rmb on the adapter's icon, then choose disable. You can re-enable later) then it seems that Pro/E will use that address fine in the future, even if you have two NIC's. No guarantees on that one, tho.
It is NOT true that unless you are "using" the NIC, pro/e won't be able to use it. First, the cable modem is only a modem. The connection STILL has to go through the network interface card. If you're using cable you ARE using your NIC. Second, the computer is aware of the hardware even if it isn't being used. In the olden dayes before everyone was internetted people often had to install NIC's just for the MAC address for copy protection. I don't remember where to look for the MAC address, but free IP tools such as WinIP will be able to suss it out for you. Then look in your license file that came from PTC. Your MAC address should match the number in the license file.
A couple hints : don't install Pro/E or ANYTHING into "My Programs" or wherever the H Microsoft insists on putting them. I put the os on one partition, the apps on a second, and the data on a third. When it comes cleanup time life is MUCH easier that way. I have a directory on the apps partition for licenses. Back it up. When you get the Pro and your other apps running nicely, zip 'em up and save the zip somewhere. Then when something Bad happens, format the partition and unzip 'em. Or if it's just a Minor Bad, erase the blown directory, defrag the drive (NTFS sucks) and unzip. Back again in business in less than twenty minutes. Much quicker, easier, and less stressful than trying to figure out how the hell Bill's Little Creation barfed *this* time when your back was turned.