Sera, this sounds like a problem we have seen before. It seems there are some specific 350Z's where the ABS ecu throws a wobbly if it doesnot get an acknowledge from the engine ecu within a few mS of power up. It is thought the Link ECU takes slightly longer than the factory ECU to send out CAN messages after boot up. It seems rare but I remember seeing 2 or 3 cases in the few years I worked for Link.
The fix is to wire a relay in to the ABS ecu power supply wiring, so during cranking the ABS ecu power is cut - it then reboots, gets its acknowledge from the engine ecu straight away and is all happy. I will PM you a document describing what needs to be done.
