Problem with cordless mouse/Keyboard combo set

[Lennon Cook]

I am attempting to use my Omni cordless mouse and keyboard set - these
both connect with the same receiver, which plugs into the computer
with a single USB cable. The keyboard works fine - the mouse, however,
does not work at all. It does not move the cursor, and clicks aren't
registered. Testing with a different (corded) USB mouse works well.

For what reasons might two devices on the same physical connection
give this discrepency in workingness? Is such a setup simply not
supported, or otherwise is there anything I can do to find out more
about what's going on here?

--
Lennon Victor Cook
"He who receives an idea from me receives without lessening, as he who
lights his candle at mine receives light without darkening" - Thomas
Jefferson