I have the same problem with my Spica using the My Track application. It can log the track only if I configure the display to never turn off. I tried G1 before with My Track, that worked just fine.
In GPS Test the SNR is never better then "yellow", the time cannot be read from the GPS module.
Additionally the G sensors are not calibrated and cannot be calibrated. Only if the application can calibrate it. But for example Layar cannot.
After using the phone for one week I'm really disappointed.