Android phone/Pandora/stereo set-up

The "rings" as you call it are either mono (2 rings) or stereo (3 rings).

You still should have gotten at least one channel using
the mono cable? Was it pressed all the way into the jack?

Here are several choices for such cables.

Also, most all the major cable companies either have or
can make you one of these.

3.5mm jacks are not all the same, even if they have the same number of rings. You need to get a 4 conductor cable.

"You still should have gotten at least one channel using
the mono cable? Was it pressed all the way into the jack?"

Not in this case. Mono is 3 conductors, not 2. And stereo is 4 conductors, not 3. You need to get a cable that has 3 rings and is labelled TRRS. If it doesn't say TRRS, the cable won't work.

Radio shack has what you need.about $8 depending on length

Do you have a protective case on your phone? If so that could be the problem as it will prevent the cable from going in all the way.