Crack it open and replace electrolytic capacitors (those round cylinder things) -- those things always fail. NOTE: REMEMBER TO OBSERVE POLARITY or you will destroy your new capacitors.
Next, check resistors and replace any that are out of tolerance (you can check these in-circuit with an ohm-meter). I assume a diode or two may have also given up the ghost...you can check those with an ohm-meter also.
You shouldn't NEVER plug in old electronics it in like that....especially if it's been out of service for so long!!!
I don't know if there's a transformer in these things, but if there is, you should have plugged the power supply in series with a 60 watt lightbulb in order to limit the current.
If the bulb glows brightly, then your transformer probably has a short-circuit in the primary.
That yellow crud may be wax from the transformer...no way of knowing until you open the case.
If you plan on doing any soldering, use a 30-watt soldering iron and ROSIN CORE solder (not acid core) available at any hardware or electronics store - also use a heat-sink (a pair of locking hemostats are good for this) . This should be enough for most electronics.
Anything higher and you could scorch your circuit board and the components.
P.S.: What do you do with such an old machine? Do you collect them?