Ok, am assuming you have the following...
SPH-D700-DI18-8Gb-REL.tar.md5
20100512.pit (I have never used the 528.pit file to flash DI18 back on to the phone, only the 512.pit file, which is why I listed it here)
I am going to assume the newer v1.61 of Odin which you have will work ok with the above pit file, but it is only an assumption.
(Listing all steps just for the sake of having it all together, not trying to imply you were doing anything incorrectly)
Pull the battery from your phone and restart your computer. When it is all booted up, start odin and load the .tar.md5 (PDA section) and .pit (the PIT section) files into their respective places. Also make sure that only 'Reboot' is checked.
Next, insert the battery into your phone and boot into download mode (keyboard '1' + the 'Power' button). After it has entered 'Download' mode, then connect your phone to the computer with the usb cable. You should now see a COM port in Odin, if you dont, you need to try a different USB cable or port and try again until you do. If you have exhausted your available options with possible USB cables/ports, you may want to try uninstalling/reinstalling the drivers and trying again (if somehow you installed kies, I recall reading that at least one other person had an issue with it being installed, so try uninstalling that too).
As soon as your phone is recognized by Odin, hit the Start button and wait for it to finish. If it fails, pull the battery of your phone, close Odin, restart phone and Odin, and try, try again (following the same steps as above).
Addition: If your still having issues getting your device recognized, you can try 'uninstalling' the Epic or any 'Unknown Hardware' (have to make sure the phone is connected to do this) from the Device Manager in Windows, just make sure you also click the box to 'Delete the driver software for this device' if possible. When you have removed the Epic from the Device Manager, unplug your phone, reinstall the drivers, then plug your phone back in to see if it loads the correct drivers and recognizes it. When in download mode, the items in the Device Manager will be 'Modems->SAMSUNG Mobile Modem' and 'Universal Serial Bus controllers->SAMSUNG USB Composite Device'