(note: I'm going to explain a lot of issues ― but I only care about having an Internet Connection with the newly installed F96; so you don't have to waste time on thinking about how to solve the rest of the issues and details, but they are likely important to mention)
It all started from a computer I bought a few years back. It came with an inner SSD. I installed FossaPup 9.0.5 from the same ISO file, on a Flash Card and the inner SSD. I normally used the SSD as my OS. The SSD stopped working a while ago. I want to send it to a Lab. But strange things happen when I remove it, which make it impossible to use the computer without it plugged:
• Since it stopped working ― I'm normally using the Flash Card OS, with a new Save File I created on an External HDD. I can't boot it without the SSD being inside the computer. Specifically: it goes through the whole process of booting, and right at the end - the black screen with the blinking underscore at the top-left corner - just stays; and when I click on the Power Button of the computer - there's a message about Puppy shutting down, and it does so. So it's like - the final Graphical Interface - doesn't start. A Computer Technician gave a hypothesis ― that the SSD partially works, and contains some booting files, or something similar. And because it's the same system in the Flash Card ― I can't boot it without the SSD inside.
• I now installed F96 on another Flash Key and another new HDD. Here - some new issues come up. Some are the opposite; for instance ― when I boot the HDD, with the SSD plugged ― the same thing happens - with the black screen and underscore (with the SSD unplugged, in the other case).
• The F96 HDD and Flash Card - boot without the SSD ― but without an Internet Connection. I tried to boot the HDD and Card with the SSD unplugged, many times ― and it's always without Internet Connection.
• The F96 HDD with the SSD inside - doesn't boot ― but the Card does; and with Internet Connection.
• So I need to boot the HDD (and\or Card) - without the SSD, and with Internet Connection. Why would the Internet Connection be related to the SSD? BTW - I know I can remove the SSD, with FossaPup 9.0.5 running ― and it continues to work, and the Internet Connection stays.
Another detail: with the SSD inside:
• In the beginning - I have to click on ESC or DEL to enter Bios - to select which device to boot. When the SSD is unplugged ― it just boots.
• And everything happens super slowly. Without it - fast.
(edit) Continue from this comment, where I found additional information (and skip irrelevant comments).