most higher end integra's have a input level adjusment or input selection for each and every input. Perhaps you are not on the correct input, go to onscreen programming and check out the input level and input select - also try the tape in another input like tape 2 or cd. It will not hurt the receiver for a test. Also, if you are using the cheap cables from the manufacturer - try a pair of cables that you know work or go by some. BTW, you don't need to spend $40 for cables order them online through amazon or other store. Gold / sliver plated oxygen free are best.
Please unplug the unit from the outlet for 15 mins and then check if the symptoms still there.
Reset the unit to factory setting by following the steps below.
> Power on the unit.
> Press VCR/DVR button key + On/standby key at the same time to re-initialized the memory to factory settings.
Check also if the remote control is working fine. Aim the sensor of the remote control directly to your cellphone camera, while pressing any button key from the remote control (button key with an issue) you will be able to see the flash of an infrared emitted by the remote control indicating that it is working fine. Watch the video below for more info.
First of all you have to check the speakers impedance. It should be 8 Ohms.
if the Ohms of the speaker is lower than 8 Ohms, it will overload the amplifier and will over heated and will switch off to prevent further damages. try to use speakers which have impedance of 8 ohms.
http://www.integrahometheater.com/faqs.php Check the connections and try a master reset?
Perform a master reset. To do the reset you need to turn the receiver on, then on the front panel of the receiver press and hold the "VCR/DVR" button while doing that press the "STANDBY/ON" button. You will see the word "Clear" in the display screen and the receiver will go into standby mode.