Your symptoms sound like a loose connection or other power problem, as others have also suggested. The only time I have seen this sort of behavior is when my battery is about to die. But, given the things you have tried to fix this, it is sounding more like a flaky board. I hope the replacement does the trick.
Off the top of my head, here are some troubleshooting tips for the usual types of problems.
**Power problems
If the green LED suddenly turns on solid and the serovs stop moving, there is probably a power problem. Weak battery, loose connection, short circuit, etc.
When the logic supply drops below 4V or so the processor will reset. The internal brown-out detection will force a reset before the thing goes haywire. The symptom of a processor reset is that the green LED will come on solid and the servo outputs will all turn off. If you are using the same battery for servos and logic, a weak battery might cause a reset whenever you send a move command. This is because the additional current draw from the servo pulls the battery voltage down causing a reset.
**Communication Problems
If the green LED never turns off when you send a command, you have a communication problem. Mismatched Baud rates, disconnected serial cable, wrong COM port, etc.
After power-up, the green LED stays on until the first valid character is received over the serial port, at which time it turns off. Thereafter, it blinks briefly for each received character. If the serial data is being corrupted somehow, the LED will fail to blink for bad characters (framing errors).
My usual sanity check for good communication is to use the VER command, which causes the SSC32 to reply with the firmware version number. It should work consistently.
**Servos Don’t Work
This is a lot less common than the first two. If you are using a separate servo supply, check the voltage on the servo header pins. Also, check the firmware version to make sure that you have the firmware for servos 0-31. There is a firmware version for servos 32-63; if you have that installed by accident it could be very confusing. Try connecting a different servo to the pin to make sure the servo is working. Make sure the servo connector is not connected backwards.
Good luck with this. I know from experience how frustrating it is when things don’t work the way they are supposed to–especially when it is something new and you are not 100% certain how it is supposed to work.