Can you please list all of the connections that are involved?
What kind of video and audio outs does your Xbox have?
If it has VGA, I would suggest connecting the VGA out to the VGA in on your hp monitor.
Otherwise (I.e. if you have VGA video out) you'd need some kind of other just-video out on your Xbox to adapt to dvi or VGA
That way, the Xbox doesn't think it's sending out sound through the HDMI connection.
Then, depending on your speaker system, you could use the headphone jack, or some kind of RCA output if you have one on your Xbox.
There are adapters for just about anything out there, such as 1/4in to RCA or dvi to VGA, so there is little chance that there is no way it would work out.
Anyway, to sum it up, most likely scenario you just use VGA to VGA and 1/4in audio to 1/4in audio in separate connections from the same Xbox.
Please keep us updated on how it works out, and good luck.