Latitude 3510 touchpad "buttons" stopped working

Dear community,

Hope someone may have some hints here. I've got a brand new Latitude 3510 (a handful of months old). Last week, both the left and the right touchpad "buttons" (i.e. the lower-left and lower-right corners of the touchpad) stopped working, with the result that, for example, I cannot select text anymore by clicking-and-dragging.

I've installed all the available Windows updates (I'm on Windows 10) and the Dell updates, and I've run the boot diagnostics - which yielded 100% success. Device Manager doesn't show any particular touchpad drivers, there's only the Windows-provided "HID-compliant mouse" and "PS/2 Compatible Mouse" devices.

Is this a software issue, or is it a hardware failure? Anyone experienced anything similar?

Thanks so much in advance for any pointers!