If the answerphone is connected to the Phone Port of the OBi, then that does confirm that RingDetect is ok and the Phone Port is putting some sort of ringing out to the attached phones.
Testing with a simple corded phone would be the best idea. I wonder if the existing phone is adjustable to receive different ringing patterns? The OBi is very configurable for ringing patterns. Under Ring Profile B there are ten different ring patterns. The ring pattern to ring the Phone Port is set on whichever service the incoming call is received on. For an OBi110 sp1, sp2 and Line Port are all set up independantly. For instance to set ring pattern for incoming calls on sp1 set:
Voice Services > SP1 Service > X_RingProfile: B
Voice Services > SP1 Service > X_DefaultRing: n
n = pattern number 1 to 10.
I'm guessing that the devices are set to Profile B (Australian), DefaultRing 1 (default).
DefaultRing 1 is the same as UK standard ringing (I use it myself here in UK for one of my services). It has two rings of .4 seconds followed by a 2 second gap. Maybe the attached phones prefer a longer ring before the gap. You might experiment by trying different X_DefaultRing settings, or simply switch to X_RingProfile A which will give North American style ringing. Maybe the phones were manufactured with North American standards in mind.
Anyhow, there are a few things to try.