Hmm, interesting. In as much as you likely will not like this answer, if this were my setup, I'd pull the Alpine first and plug back in the original head unit and then try the antenna. Something you didn't alude to was whether you had antenna issues with the first radio. I think you need to diagnose whether it's the antenna or radio.
If the old radio is clear and the Alpine isn't, the Alpine might be faulty, or might need a separate ground to help. If the antenna is bad on both, then it sounds like either a) the cable is bad on the connection to the base of the antenna, or the cable is broken.
Do you have an electrical meter and are you familiar with testing for continuity? If you are, check the antenna lead against the antenna mast and then check the antenna's outer connection against ground I think it is. If neither works, you have a problem with that cable.
That's at least where I'd be looking and hoping I'm on the right track.