This is what happened with me. I tried to do some digging, looking for names, references, but with little luck. Their facebook page appears to be fanmade; the logo is literally made in crayon and the youtube links to a guy called Raptor Roth, who was mentioned earlier in the topic.
BS01 does provide some names, although no sources are given.
In 2005, a pair of songs were released on the official BIONICLE website. The tracks - "Hero" and "Caught in a Dream" were written and produced by Morten Krog Helgesen and performed by the band All Insane Kids, commonly abbreviated to AIK, with vocals by Christian Bastian.
While it's clear they were formed and disbanded by LEGO, it can also be assumed that they were Danish in origin. Morten Krog Helgesen is a Danish name, AIK was commissioned by LEGO - Danish company, and Cryoshell is also a danish band. Furthermore, some of the lyrics seem a bit awkward, like english wasn't their primary language. This is more apparent in the demos which had slightly different lyrics that were corrected in the official versions.
"To grow up and strong and redo wrong."
"Is my senses my playing a trick on me? "
I also looked up some of the other bands whose songs were used. While All American Rejects and Daughtry are relatively known bands, Presence, whose song "Ride" was played during TLR's closing credits, are mostly unknown. Researching them is a bit difficult as there are several unknown bands also called "Presence," but I did find an article discussing them. The band, however, appears to have disbanded. Their latest album, which also contained "Ride," was released in 2007, two years before TLR and way too long to still be active.
Interestingly, BS01 says Presence is a Canadian band, but the sources I found says the're from Florida. My sources could be wrong but BS01 didn't list any citations.
Now that's settled, only one great mystery is left. Who. Made. Piraka. Rap. It's one of BIONICLE's most (in)famous songs but no names are attached to it. Which may be for the best, really.