My dongle is plugged into an external, powered, hub - which in turn is plugged into a single USB port on the PC. Just out of curiosity does the above apply, or is plugging into any of the ports [on the hub] seen as "the same" from the PC's perspective?
"If you want you can post me up all your nice molded pluggable sensors to test and I'll swap them for my perfectly working solder and sellotape cables"
No Deal!
Shame on the sensor swap...

for a machine with just one USB port, it would most likely just have one (onboard) hub. SO the drivers on different ports issue shouldn't matter.
However if it just has one port how old is it? I have a laptop circa 1998 with just one USB port. And what version of windows are you running on the machine? IIRC then the original Windows 98 had some additional stuff in the service pack on the install CD for USB support. Whilst in later versions of Windows 98 USB support was bundled as part of the OS install. From that point on all versions of windows had fairly good USB support with the exception of Millenium which was just awful all round. But that is just a digression and a bit of a red herring.
I presume you've tried the dongle direct into the port bypassing the external powered hub? DH maybe right in that it is a power issue.
The fault may lie with your RJxx to RJxx adaptor but I doubt it, unless it has suffered pin damage. My money is still on a corrupt driver.
Do try the dongle in another machine....