"I can't find a schematic and cannot get the value of capacitors C356 & C358."

https://www.ssguitar.com/index.php?action=dlattach;topic=3805.0;attach=5777

C356 & C358 are .015/ 600V capacitors.

If the power supply cycles on & off that means it is trying to start but something is preventing it from doing so.
Typically, a short on the secondary side will do that.

By the way, this is a Switch Mode Power Supply.
If you have no experience with these it is in your best interest to take it too someone who does.

The TDA can be safely operated without a load on the output.

Huh.
You want to sound like Stevie Ray Vaughn.
That is admirable.

These amps are from the late 80's so the distortion channel is NOT going to be want you want it to be.

That said, the Clean channel is very pedal friendly.

Marshall 5010 schematic:

How about a schematic snip of the circuit?

The Spyder III used a TDA2050 for the output section.

As far as I know that part is no longer manufactured.

You could try an LM1875 though.

There are more than a few germanium transistors in that amplifier.
Prove that they are bad before replacing them.

I would think 'capacitors' in a non functioning Tremelo circuit.

Before adjusting the 'bias' of the output section, I would suggest that you measure where it is set at the moment.

Measure the voltage (in MV's) across either R14 or R15 (the ballast resistors).

There is not a Fender specified bias level on the schematic.

Adjusting P2-B potentiometer will either increase or decrease the current draw of the output section at idle.

Being a Class A/B output I would go for the lowest setting that just gets it out of crossover (Class B) distortion.

Before condemning the power transformer, try this.

Take the power cord and put an ohmmeter across the male tines.
Turn the power switch on & off.
With the switch On, you should be reading the power transformer primary coil.
If no reading is shown, you need to isolate that issue.

There are five components.
The cord itself
The mains fuse (110V/ 5 A__220V/ 2.5A)
Two in series thermistors
The transformer primary

If the reading is good, then you need to disconnect the power transformer secondaries and measure the winding resistance.
Mark down where they go!

P16_P15_P14 is the high voltage winding
P19-P17 is the heater winding

If all of this checks out and with the leads still unconnected, you should get the secondary voltages required.
If the voltages check good, then it's Not the transformer and it's time to move on to the circuit board.

The amp may be unstable & is oscillating at a high frequency (above hearing)
A scope should show that.

Kind of difficult to help without a schematic.

IF the gain control is in the feedback loop of an op amp, you may be able to tone it down with a larger potentiometer value.

The first reverb circuit transistor, on the left, (3904) has weird dc voltages.
The collector and the emitter are the same voltage.
It may be shorted.

This circuit is an amplifier.
It should be able to drive a speaker.
That said, the -7Vdc on the tank coil is not a good sign.
I would expect zero volts dc.

Nice find on the L3 schematic, PE.

It appears that R9 is a variable resistor for idle current adjustment.

Measuring the voltage drop across R16, 0.22 ohm ballast resistor, will give you your bias voltage.

I can't seem to put my finger on the L3 schematic.

If it is anything like the L5/L7, then the bias is fixed.
3mv across any output ballast resistor.
http://www.rru.com/~meo/Guitar/Amps/Lab/schem.html

Please post the schematic.

Those 'sandbox resistors' are most probably the output ballast resistors.
The speaker output is taken off of them.
Therefore there should be zero dc voltage on them.