Sounds like a malfunctioning VSC computer, or a loose connection on the wiring connector to the VSC unit.
The VSC computer doesn't just handle VSC, but it also does ABS, vehicle speed monitoring and brake system safety checking.
The lights work as follows: the VSC light comes on, if the VSC computer sends a "VSC not available" signal to the dash. No signal. No VSC warning.
The brake light and ABS light stay on, unless the VSC computer sends a "brake system safe" signal or "ABS system working" signal. No signals, the lights come on.
The speedo takes its signal from the VSC computer as well. No signal from the VSC computer, speedo reads zero.
Finally, the power steering system takes a speed signal from the VSC computer so that it can adjust the power assistance. If it gets no signal, then it will report a power steering fault and may not work correctly.