I seriously doubt that IRQ sharing is a problem - IRQ problems have been
ironed out by the hardware and OS since the Win98SE era. If the dongle
does not invoke a port, perhaps there is some source of RF interference
with the dongle on the problem computer or a USB port power problem? RF
interference with a wireless ethernet adapter, mouse, etc. on that
computer, or some app running in the background taking CPU cycles, etc.
If you are not using the modem, you can disable or, perhaps, deinstall
it as a test?