No microphone listed in Device Manager

A friend's mother has been having trouble with Zoom. The webcam works fine but there is no output audio from her laptop. I talked her through a few diagnostic steps, the main one being to have a look at Device Manager. There is no microphone listed. When she opens Zoom she gets a message saying that no microphone has been detected. Is it possible that there isn't one installed? I naively thought that all laptops had one but I could be wrong. She says it's a reconditioned laptop over 6 years old - she can't find a model number or even a maker! I did all this over Zoom with her on the other end of the phone so sorry that the information is a bit patchy. It's a Win10 machine with all updates done (allegedly). I've suggested a plug-in USB one which seems the best solution.

havent got a clue but suspect iff it is that old it will probably be short in usb ports but have earpiece/speaker/headset mini jacks

Looks like you've run through decent enough checks.

If you bring up the sound properties in control panel, it shows you somewhere whether the default recording device is enabled. Perhaps its disabled, which then might not show as an obvs error in device manager.

USB Headset from a firm like Trust would be a good fix IMO

I would have thought that any laptop which has a built in webcam would also have a built in mic, too.

Check in the BIOS whether it has been deactivated in there. If it has, Device Manager won't see it and cannot enable it.