Nope. If you can hear the alerts at full volume, then you should be able to hear CDs at the same volume. The only things that would make them different would be a software setting, a faulty or mis-placed cable, a faulty connection on the motherboard or on the CD drive, or a faulty drive.
I don't think a fault in the motherboard sound IC is indicated if the alerts are OK, but I could be wrong. It could be a bad motherboard trace somewhere, I guess.
So I'll put down a few suggestions here; try them in order and let us know what you get.
First off - thoroughly explore the Sound control panel. I don't recall 7.6 very well, but it should have separate volumes for alerts and other audio, tick boxes for CD play through (or some such term) - anyway, have a good poke around in there. There's a tick box for where CD audio should go - to the internal speaker or to the speaker jack at the rear.
By 7.6, do you mean 7.6.1? If not, it would be a good idea to download the free update. Dunno if it will help with this particular problem, but it's a good idea in general and worth a bash.
If that doesn't work, tell us exactly which pins the CD audio cable is connected to at both ends.
Connecting external speakers shouldn't make any difference, unless that box is ticked.
Does the drive have a headphone socket on the front? If so, stick some phones in there and see what you get.
There should be three cables to the drive - audio, power and SCSI. The audio cable won't always be about a centimeter (half-inch) wide, sometimes it's just two or three strands - depends on the Mac. Test, or get someone to test, the cable for continuity and shorts with a multimeter.
If all of the above fails we can take it from there.