We repaired the Squeezebox today! In case anyone else has a similar problem, I'll describe how we did it.
The VFD on the Squeezebox version 2 is a standard Noritake module that needs a 55V anode power supply. This anode supply was at zero, so we knew roughly where to look. It's a switch-mode supply that takes 5V and uses an NJM2377 SMPSU chip and a BSP296 MOSFET to generate 55V. We put the scope (Tek 5440) on the drain pin of the FET, which was at 5V with no switching. The gate pin also showed no switching. The oscillator section of the NJM2377 (pin 7) was working at 250kHz, and the voltage reference was OK at 1.5V (pin 8 ). We traced the circuit on the PCB and noted some resistor values. We began to look at sources for a replacement chip and MOSFET.
Something odd happened, though. The bench power supply (Farnell D30 2T) made a brief buzzing sound when the device was switched on, for maybe a quarter of a second. This made me think it was getting overloaded (it's 2A and the original Squeezebox PSU was 1A). So we held the scope probe on the MOSFET gate again, while switching on. We saw a brief burst of switching then nothing. Aha! the NJM2377 is sensing an overload and shutting down! Now we checked more carefully around the output side, where the VFD's anode is connected.
We found about 120 Ohms between the anode pin and ground, and the resistance changed slightly when we reversed the multimeter leads (HP 3466A). I suspected the VFD at this point, but Kate suggested that we desolder a tiny surface-mount ceramic capacitor (C2) that's across anode and ground. Sure enough, the ceramic capacitor was partially shorted. We put it on the capacitance bridge (HP 4260A) and it balanced at about 33nF. The DMM (Vichy VC99) could not read it at all. So, having found a 40nF disc ceramic in the junk-box, we fitted a temporary replacement. The Squeezebox powered up with a splendid display of VFD graphics!
So, the lessons here are: always check the simple stuff (excessive load on SMPSU) and listen for even the tiniest clues (bench PSU overload buzz).