Indeed, a nice winter project. I did something similar to a Ferrograph Series 6 I have. Nice to keep the old stuff working. If a coupling capacitor fails open circuit, then the result is usually silence. If it fails short-circuit, then the result is also usually silence, but then as well, the following valve will glow bright red as the current through the valve rises rapidly, and also burns out the cathode and anode resistors. If the following valve is an output valve like an EL84, then the output transformer suffers too.
If none of the valves are unusually bright, and nothing is visibly burnt out, then a poke around with a multimeter measuring voltages on the valve anodes, cathodes and grids and compare with what the service manual says they should be, (+-10% or so) will give you fair idea where the problem lies.
Also, with these early domestic machines, they had fairly complicated switching between play and record as in those days labour was cheap and components expensive, so they tried to avoid using more bits than they had to. These switches may be worn or even broken, so it may not be entirely electronic, it could be semi-mechanical. If the sound cut out whilst you were playing, it sounds to me more electronic, but if it just wouldn't start playing from stopped, then I'd look at mechanical as well.
S.