As you say, there doesn't appear to be any problem with comms between the Zaurus and GPS device, because you're picking up NMEA data on ttyS3. However, the NMEA data is showing that you are not picking up any satellites.
If this is the first time you've used the Ambicom, it can take a while to get a fixed position. I suggest keep trying for half an hour and make sure you're in an open space with no obstructions.
I've also experienced this "no fix" problem on my Z in the past and found that restarting gpsd will fix it :
$ killall gpsd
... then restart it from within qpeGPS.
As a last resort, see if you can get the Ambicom running with another portable device.
Ian