It's been a *LOONG* time since I messed with car audio...BUT if memory serves:
You don't say exactly how you hooked the known-good CD player up, whether you came from a headset jack, speaker-out terminals or RCA jacks, so forgive me if I'm covering ground you've already covered.
The RCA-style input is not the same as standard output from a speaker or headphone jack. I don't remember what the impedance is, but I'm thinking it's significantly different than what you get from a speaker wire. As I remember, you couldn't just go from the audio outputs from the head-unit, unless it was either native RCA or you used a converter.
To bench test an amp, I would use a phono (dating myself here) or CD player with native RCA outputs. If you're getting no audio from known good input and known good speakers (are they 4 ohm? Many car amps are looking for 4 ohm loads).
I'd also check your power source and put a meter across the terminals to ensure it's pulling some load. As I remember most older amps would "pop" the speaker when they powered up -- the 'soft start' is a newer feature...but as I type that, I'm thinking that the "pop" may have come from the head-unit instead of the amp, because thinking of the startup sequence we used to use for auditorium audio (not car audio) we powered the mixer, THEN the amps or we rattled windows with the POP.
Most of what I'm telling you is old, and I was in high school last time I wired a auto sound system, and it's been probably 10 years since I ran a mixer board...I'm sure someone here is both more knowledgeable and "fresher" with it than I am.
Hopefully it can give you a start...