Usually you don't want both lights to be solid... the green light on your motherboard should be solid signifying that there is a connection, but the orange light should be constantly flickering signifying that data is transmitting.
Most modern modems won't have a solid green light rather a flickering one signifying that there is data being transmitted.
Again, as Ralston said the following information would be beneficial to troubleshooting:
Make/model of router:
Make/model of modem:
Motherboard make/model:
(or make and model of pre-built system)
On top of installing your motherboard's NIC/LAN drivers, you might want to try and just reset your router to default factory settings.