Mr Draper Sir,
I'm not surprised by what you are seeing. If the desktop & loptop machines are "old" then the earlier USB chipsets were notorious for power handling, and these USB based internet modems tend to be power hungry. I had an Acer laptop that had major problems with USB modems. Modern hardware is much more freindly towards USB power hogs (USB coffee mug warmers, USB fans, USB Broadband modems etc)
Also Win98 is not good with USB, so any modern USB device that does anything remotely sophisticated could bamboozle Win98.
The latest BlueYonder USB device may well be different enough internally to cause a problem whcih accounts for your BT working then BlueYonder not on a new modem.
Sad to say, but my advice is to get a router if funds allow & let that talk to the Broadband line. Then use Ethernet which is much older & more robust. It frees up the PC from having to talk to the broadband line.