Yes the FLASH of a new processor will be empty.
Was the system still somewhat working? If the FLASH of the original is still in tact and not locked it might be possible to extract the code with JTAG.
If it is locked or the processor is fully dead then you are out of luck and need to contact the company who made the board.
An EEprom is normally only used for some parameter storage and not firmware, due to them being small in memory size and lack of speed.