That is an old model, with features set up quite differently from most current models. For people who are having trouble with a basic search, here it is:
DSP-A3090 - Amplifiers - Hi-Fi Components - Audio & Visual - Products - Yamaha United States
What source are you trying to play? It may be that you need to set the "trim" control differently for the input you are using (see page 14 of the manual).
There are also unusual controls on the back; you may need to adjust the Main Level control (p. 21 of the manual).
You should try it with the processing effects off (see p. 51).
There may be other things to adjust as well as checking on all of the connections. You should spend some quality time reading the manual, as it is quite different from current models.
Also, make sure you turn down the volume to test before adjusting something else, as the volume all the way up could be a serious problem for you if you correct your issue.
Before I read more in the manual, I will want to know how everything is hooked up, as there could be a problem there.
Edited to add:
Your description fits with accidentally pushing in the Tape button on the Bose EQ, as that should ideally completely cut off the sound, though often a tiny bit bleeds through.