There are two tape monitor switches on the front panel If either of these is activated without a tape deck plugged into the corresponding tape input on the back panel (or other line-level device, such as a cd player), there will be no signal being fed into the amp, and therefore nothing coming out of the amp. Simply put, activating the tape monitor switch is telling the amp that it should look for input from the tape monitor input connections (and only from those connections). Obviously, if there is no input there, the amp will be silent....or near silent; sometimes, if there is another source component connected and playing (such a cd player), a bit of its signal will bleed into the selected input, producing very faint output.
Regarding your question about problems with headphone output; in this unit, the headphones are fed by the same output circuit as the speakers (padded with resistors to drop the voltage). So it would be expected that problems with speaker output would be seen in headphone output as well. This is not an indication of problems in the preamp section.
Regarding your question about multiple speakers; this amp was designed to handle, at minimum, a 4 ohm load. Anything below that will stress the power supply and output circuit. Speakers present a "load" to the amp, determined by their impedance. The lower the impedance, the greater the current draw. For example, 4 ohm speakers draw twice the current of 8 ohm speakers.
Two 8 ohm speakers on the same circuit (same channel) = a 4 ohm load. Four 8 ohm speakers on the same circuit = a 2 ohm load. Two 4 ohm speakers = a 2 ohm load. Etc, etc.
The lower the impedance load, the higher the current draw. The higher the current draw, the more likely it becomes that you will have damage in the output circuit. Modern amps have various safeguards to protect the amp in the such situations, but on older units such as the SA-7100, protection is not nearly as robust. When you turn the unit on, are you seeing the protection light come on? It should come on for a few seconds. then go off. If it stays lit, it is an indication of a short in the output circuit.
There is some (very) small chance that dirt/oxidation in a selector switch (such as the tape monitor switches or tone defeat switch) or potentiometer (such as the volume control or tone controls) is the culprit, which is why the first advice given to folks having similar problems is to open up the unit and clean the switches and potentiometers (pots). Here is a link on that topic:
http://audiokarma.org/forums/index.php?threads/the-idiots-guide-to-using-deoxit-revisited.207005/
While always a good idea with an older unit, given your symptoms and history, it is very unlikely that cleaning the controls will resolve your problem.
Do you have a digital multimeter?
