Please call FAST tech support and ask for an RMA number so you can send the ECU in for repair. There is almost surely a damaged ground-related circuit inside the ECU. When you connect the handheld, the ECU gets a ground through that and it band-aids the issue.
I've seen what you described happen once. The EZ-EFI installation was sound. Battery wires straight to battery, etc. In fact, it had been running well for some time. One day, the engine wouldn't crank over. The car's main battery cables were kind of shady. They looked fine but turned out to be mostly burnt out on one end. It took some wiggling to get a connection. Somewhere in the process of keying on and off, attempting to crank, fiddling with the battery cables, etc., the ECU must have been hurt. After that, it acted crazy if the handheld was disconnected. If I remember right, it was also discovered that the engine did not have a good ground connection to the frame or battery. Not sure if that was a factor.
I'm not saying that is what happened to yours. Maybe a component on the board just gave up the ghost. Either way, I wouldn't go much further without getting the ECU checked out.
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