If I understand your information, you are saying that when the tape deck is selected as the source on your stereo/receiver, there is hum, or hiss. This noise gets worse when a tape is played?
If so... I would suggest that the filter capacitors in the power supply are bad. When there is no load, as when no tape is playing, there is hum from the power supply, when you play a tape, the load on the power supply is greater, so the humm gets louder.
Hiss is usually noise in the preamp circuits, but this can be indirectly caused by a bad power supply also, as mentioned above.