With older firmware there was no blue LED flashing in fastboot mode, so this could be normal depending on the OS version you’re coming from.
Whether your laptop “doesn’t see the device” depends on the definition of “see”.
When in fastboot mode, file explorers or sync programs will not be able to “see” the phone. The fastboot command on the laptop, however, should be able to “see” it.
Try the steps 1. and 2. here to get fastboot going … and report any errors with this …