I'll try my best not to sound like an '80s/'90s-era video geek...
Sounds to me like you recorded the tape either without a clean video signal (you had an audio input but had no "burst" on the video)-- or maybe even without a "control track." If the machine you taped this on was made after the late '80s, chances are there is a control track no matter what. The unit you're trying to play this on is probably a newer one; some of them get finicky when trying to play a tape without a video signal-- and automatically cut the audio out to avoid the consumer's having to hear the obnoxious "roaring" sound. When you pull up the unit's own menu, you're likely "tricking" the machine by giving it a temporary video signal-- unmuting the audio for the time being.
Before transferring the audio, I'd find a different VCR for playback. If you recorded it in Hi-Fi (it'll sound like crap if you didn't), the sound information is actually embedded in the video track-- not the audio one. To get the fidelity, you'll need a VHS machine that'll play the full video track even if it has no signal to lock onto. Tracking will be problematic, but not impossible.
That all being said...
Injecting the Philadelphia Radio content back into the thread, what pray tell was WOGL running in 2003 that was so amazing people are asking you to "share the wealth" online? I can't imagine anything of earth-shattering import that could be worth preserving on that tape, aside from the obvious possibility a Hyski or Nettleton shift is included. And even then, this would be around the time this radio station began to sound very, very boring.
But to each his own. Good luck with the transfer.