Is there any way to record songs on your computer, onto a
tape? Please Help.
Sure. Use or split off one of the "line out"'s on the back of your soundcard and run those into your tape deck. You may have to get an adapter to convert to speaker plugs from the mini jack. Those are available at most stores that carry audio equipment.
You can hear the tape deck through your computer by simply running lines from the "out"'s of tape deck into the "line in" plug or plugs on your soundcard. Again, you may need an adapter to go from a speaker plug to a mini jack.
Hope that helps.
I've tried using an adapter from my 'headphone out' jack on my laptop to my RCA jacks on my receiver, but the sound is horrible --- clipped and ugly
Depends on which RCA jacks you use on your hi-fi. If you use the phono jacks, yes it will sound clipped and ugly. Use one of the line inputs (AUX, Tape, CD, Video, etc.) and you should be alright.
You might have to reduce the volume level using your computer's volume control applet. Headphone outputs are a little "hotter" than standard line outputs.
HTH
Fred N