My taskbar was working fine until signing on the internet, so I assume this disapparance is malware-related. What's the shortcut keystroke to make it reappear?

It isn't just hidden is it? Put the mouse cursor right down the bottom of the screen and leave it there for a second or two. Does the Taskbar re-appear? If so, right-click on it and choose 'Properties'. Un-tick the box that say 'Auto hide'.

My taskbar has disappeared a couple of times, usually when I was running too many programs simultaneously. What worked to bring it up (not permanently, but at least long enough to let me use the menu) was pressing the Windows-key on your keyboard. It's in between the Ctrl and the Alt keys, if you have it, that is...

Another possibility is if you pressed F11 which is full-screen. That often removes the lower toolbar, and you just click restore in the top right corner. Now if you've lost the top one as well, then it's not that.

It eventually reappeared after deleting some pop-up ads (several days ago they tried hiding the "X" -- Tellywellies solved that one with a registry deletion).