Squeeling can also occur if the speaker wires (especially plate wire) are placed too close to the 1st audio amplifier tube or any of the RF tubes or the antenna wires.
The switch should turn off the entire radio including the vibrator. If the switch is not faulty, check for wiring errors. Someone else may have played around with the wiring. If the switch turns off the tube filaments but not the vibrator, definitely suspect wiring changes, as there is only one switch, and it controls power to everything.
After making sure that all wiring is perfect and per the original schematic, you definitely should use a signal generator to make sure that the set is aligned properly. If the wiring has been tampered with, this is especially necessary, as someone probably tampered with the adjustments as well. If you cannot get the radio to work with a signal generator, then you need to look for open coils and such. Be sure that you replaced all condensers with proper values. Same holds true with resistors. If you see M and K in the schematic, M most likely stands for megohm. If you see M and Meg, then M stands for kiloohm. When testing condensers for shorts and leakage, one wire of the condenser being tested must be removed from the circuit. Condensers must have absolutely no leakage. They cannot leak even in the millions of ohms. The meter's needle will deflect up just slightly for most values over .001 MFD (deflection is greater for larger values). It should fall back to exactly where it started. Anything less is unacceptable leakage. Electrolytics may have leakage in the millions of ohms.
Be sure to test mica condensers for leakage as well. Never overlook them. They rarely fail, but they do fail, and sometimes they aren't really insulated with mica. There are some that actually use paper insulation, but are in the same bakelite container with the colored dots, so they look deceiving. Also, keep in mind that Zenith used Micamold resistors. If you see a mica condenser looking device that has rather low resistance, check the schematic to see that it isn't a resistor, especially if the device is in a cathode or filament circuit. The color code on these resistors reads like all other modern color banded resistors.
Thomas
The squeal (oscillation) problems could be missing tube shield(s)or not making good contact with the chassis. Alignment that is way off is less likely. All tubes except the audio output should be shielded. Squealing kills the possiblity of normal reception but wouldn't explain hum.
Richard