I had the same problem, with ip's that dont work, than i used hamachi, very simple and effective because it gives you an ip and that works perfect. Im not sure if it will work on a local network but its worth trying (you only need hamachi on the pc that hosts the server)
1) Download and install hamachi
2) Click on the on button
3) Now next to the on button you will see a bunch of numbers. The numbers before the / (example: 1.111.11.111) that will be your server ip.
4) Now you just need to go to the server.properties file there you will see server-ip: (it should be blank) there you type the hamachi adress (example: 1.111.11.111)
5) You are done! type the hamachi adress in tekkit and normally that shold work fine.