Logomatic v2 serial SD Datalogger issues
This definitely sounds like a USB issue with the computer.  The device is obviously not recognized and thus its startup can't continue past a certain point.  I'm guessing that the LEDs blinking rapidly is initial USB activity and it sounds like that isn't happening correctly. 

First, have you tried it on several computers?  Do you have any non-windows computers to try it on?

It looks like the board might incorporate several USB devices - USB mass storage being one.  If the SD card is not formatted correctly for the board then that might stop the startup of the mass storage device.  Try reformatting it again and see what happens.  I doubt it will work but you never know.

Try a different (smaller if you have it) SD card and see what happens.

If you have the programming adapter mentioned in the datasheet, attempt to re-flash the firmware or even try the alternate firmware provided.