It is not the bt module, savemiifrii would load the recovery menu if the module was bad.
If it went black after an online update, the boot2 install from 4.2 update probably failed.
Unless the wii is old and has a vulnerable boot1 (supports boot2 bootmii) you can not fix it with the infectus UNLESS you have a bootmii nand.bin or key.bin from this bricked wii. If you have the nand or key bin you can probably fix it with the nand programmer.
If the wii has not been opened up, I would call Nintendo and tell them you did an online update and now you have a wii with a black screen and you don't know why.