OK, point taken , cable switched and now I have a device and can connect to it.
The emphasis in all documentation was so heavy on using your own special extra super-cable "the Blue one", that I passed over the first, obvious solution.
Need USB3 cable, though, for the tests I am doing.

A totally new, out-of-the-box, 3404D unit is totally invisible as USB device. On 2 Windows 7 PC-s, one PC with USB3 port, one with USB2 port, it does not even turn up as general incognito USB device. Newest Picoscope SW, new unit , first start-up. Separate 5V power supply. On connecting AND disconne...