"...it may be faulty".

I concur. If it will not connect even one device, then it is obviously in need of replacement. I use a powered 2-port hub along with an unpowered 4-port hub without any problems (on a 350W machine - 4 on-board ports connect printer, keybd, and the 2 hubs).

I have read about configurations where the front USB ports were unpowered while the back ports were powered. I don't know how common was that crazy design.