Hmm it sounds like its not accepting new firmware... If you can get your hands on a spare 16f877a or 16f877-20 then you could burn the proper hex file onto it and swap the chips.
The 16f877-20 uses a file found in MPLAB called bl010101.hex
The 16F877A uses the bootloader firmware found on my site in the download directory.
Its rare to have a bad PIC but I've seen a couple.
Actually it appears to be stuck with the 16f877 firmware. Select 16f877 or 16f877a and see if it tries to download an OS. If not then it's got the right firmware.
Yes the Firefly ZIF is wired properly, just turn on #5 (on the DIP switch) and all other off. Might help for now to remove the 16F88 from the socket just to be safe.
Make sure you put it in with the notch towards the left. See the firefly documentation (recent release) for images.