some random thoughts:
HBC works fine when not launched from bootmii?
Did you reinstall HBC? or only did part of the hackmii installer like only choose to setup SD ?
Did you update or install another HBC manually ? a wad maybe?
there's an open source version of HBC, and it's using a new TitleID (OHBC) instead of the previous one (LULZ).
Bootmii needs to know the HBC's titleID to launch it, and it doesn't know OHBC.
Can you boot system menu from bootmii without black screen?
do you have bootmii.ini file on SD ? check if it's set to proper video mode.