Hi!
You will read continuity across the fuse you removed as the lamps, the mains-transformer 6.3V secondary and the five scale-illumination lamps in parallel form a continuous circuit to d.c., you'd get no lighting-up if they didn't, the five scale-lamps would measure about 30-50 ohms cold each typically!
Now, regarding your sound, (or lack of!), there is no speaker protection on this simple unit as the electrolytics C615 & C616 block the mid-point d.c. (about 21V) from pin 2 of the STK016 output amplifiers IC601/IC602.
There is a 1.6AT fuse in series with the 42V h.t. line to each of the output amplifier ICs, shown separately from the O/P board on the circuit-diagram, altho' the PCB layout diagram shows them as being tracked on the PCB itself.
If either or both fuses are blown, you will need to replace either (or both!) of the STK016s, and I recommend also replacing C615/C616 (use 1000u 50V) and C607/C608 (use 47u 50V) whenever these devices are renewed.
https://www.ebay.co.uk/itm/1pcs-STK016-STK-016-Advanced-Power-MOSFET-SIP-ZIP/253898917506?hash=item3b1d8e0682:g:NewAAOSwGs1brFWIf neither of the fuses on the output board or connected in the 42V line have failed, test for continuity from the 'OUT' pins of the output stage board to the rear loudspeaker terminals, 'SYSTEM A' and 'SYSTEM B', the '+' terminals should show continuity to the board in either position of the 'A/B' selector switch on the front panel and the '-' terminals on the loudspeaker terminal boards go direct to chassis earth/0V line.
Lack of continuity should lead to a physical examination of the wiring to and from the system selector switch itself and the condition of the wafer contacts.
If you get continuity from the 'OUT' terminals of the O/P board to the speaker terminals, connect a 1k safety resistor across the + and - terminals of each speaker terminal-board and switch your unit on - there should be NO d.c. measured across these resistors. If you get a zero or less than 0.1V d.c. reading across 1k safety resistors across the speaker terminals, it should be safe to reconnect the loudspeaker units themselves.
If you're happy with these tests so far, turn the unit to 'AUX' or 'TAPE' or detune it off a station and turn the volume control to maximum, you should hear a faint hiss/hum in each speaker if the STK016s are operational.
If no sound can be heard, place the blade of a small screwdriver on the 'IN' pins of the output amplifier board, (see layout diagram) you should get a click or louder buzz when each 'IN' terminal is touched. If this produces no sound and the fuses are not blown, the STK016s are internally open-circuit and again, it will be necessary to fit replacements.
Try this so far and if all tests well from the 'IN' terminals of your output board, you have a failure further back, which I'll go thro' in another post if necessary!
Chris Williams