@mike2060: It looks like the firmware was not actually burnt or the screenshot above is not the complete process. The firmware update process involves a couple of steps. First it burns three fuses, then it upload the firmware to the flash memory and then an EEPROM configuration is loaded. This has to be repeated for the second Atmega chip too.
If you have a look here, you can seen in the two screenshots at the end of the page that the firmware upgrade process is longer and the script that you have running there is only burning the fuses and not burning the firmware or EEPROM.
Since you had mentioned earlier that you had modified the firmware update script, can you post the updated script here so that we can have a look at it for any problems.
Also, from the same directory where you have the firmware files, can you run these commands one by one and post the screenshot here and also check from the Python script whether the firmware update did work or not :
avrdude -P usb -c avrispmkII -p m328p -U lfuse:w:0xFF:m
avrdude -P usb -c avrispmkII -p m328p -U hfuse:w:0xDA:m
avrdude -P usb -c avrispmkII -p m328p -U efuse:w:0x05:m
avrdude -P usb -c avrispmkII -p m328p -U flash:w:ATmegaBOOT_168_atmega328.hex
avrdude -P usb -c avrispmkII -p m328p -U flash:w:BrickPiFW_Compressed_Communication.cpp.hex
avrdude -P usb -c avrispmkII -p m328p -U eeprom:w:BrickPi_EEPROM_UC1.hex
Please do change the -c and -P parameter to what it is for usbasp. Also, if this works, try it for the second chip too with the last command changed to :
avrdude -P usb -c avrispmkII -p m328p -U eeprom:w:BrickPi_EEPROM_UC2.hex
Do let us know if this works for you.