By 'free lines', do you mean a physical line or a virtual (VoIP) line.
If you are using the same exact modem or voice board and you experience different results when you use your Internal extension line versus an external landline, this would probably indicate one of two things:
Either
1) The internal line is not properly set-up to ring for incoming calls as you are expecting it to be
or
2) The internal PBX line is using some kind of proprietary ring method, or is using some kind of telephone standard that the modem/voice board does not support. Analog systems can use several different methods to signal an event, they can for example reverse the polarity of the electrical current on the line, or they can send tones down the line, or they can vary the voltage that is sent across the wiring. If for example your PBX chooses to reverse the polarity to signal the ring when your modem is expecting a voltage increase, that could be the source of the problem. It's also possible the PBX is using the right signalling method, but it does not meet the detection range of the modem/voice board. For example, perhaps the modem expects a 80-85 volt spike to indicate a ring event, but your PBX is only sending 50 volts down the line, which is outside the detection range.