Umm, strike three? (borderline pitch on the outside corner

) No, I can't blame on this one -- I've revised my answer three times now. Here we go.
Okay, the 8780 has two processors. One controls the LCD and most of the buttons. This processor has an eeprom and this processor and it's Eeprom are connected to the JP1 interface. This processor is a 740 type.
The other processor controls the four learning buttons on the 8780 (1L through 4L). The LED is connected to this processor. We assume this processor is a SAM8, but since all it does is learn, we're not 100% sure.
Somehow the batteries are powering the SAM8 processor but not the 740 processor. But the JP1 interface is providiing enough power to run the 740 processor (that's why you only see the LCD display when you hook up the JP1 interface). So there's some loss of electrical continuity inside the remote. Theoretically you could hook up two wires from the batteries to pins 1&2 (Vcc or + battery terminal) and pin 3 (VGround or - battery terminal) and power the remote that way. However, someone with better electronics skill should double check this.
The MEM FAULT message means that the eeprom data is corrupted. This could be the result of a bad eeprom or just bad data. Since you already have a working 9800 and since the 9800. 8800. and 8780 are all the same remote software wise, you can download the config from your 9800 (save it in IR.exe first) and upload it to the 8780 as a test of the Eeprom. You'll get an error message in IR.exe about signatures being different, but it's okay to ignore it. If you don't see the "MEM FAULT" message on the screen than it looks like the EEprom is good.