MIDI cable in DR550 from EMU 0404.
EMU 0404 MIDI out to DR550.
You have MIDI IN on the DR550 hooked to the MIDI OUT on the Emu, right? For audio and MIDI cables, outputs always hook to inputs (never hook an input to an input, or an output to an output).
You're trying to record a pattern or a song programmed into your drum machine, right? Make sure you have HS setup as the master, and the DR550 as a slave. In HS, in Options->Project->MIDI Out, make sure the Sync is set to "Transmit MIDI Start/Stop/Continue/Clock". In your drum machine, make sure the clock is set to MIDI, and not INT or AUTO.