The problem referred in the thread title is caused by either an unshielded cable being used from the audio header to the front headphone (hint, hint…) and microphone ports; what I'm guessing is an earth loop (though created within the PC, through its own case and by the current draw of its own components); or, indeed, the combination of both. The effect of those is that, while the rear sound ports on my D945GTP work more-or-less perfectly, the design flaws in the case wiring have taken the front ports aalllllllllll the way down to being completely unusable. I do hope to repair it eventually, but it will be a while before I have the means.
To sidestep the issue
Simply unplug the front audio cable, and if it's a very old board with the AC'97 type of codec, jumper pins 5/6 and 9/10 of the header (to pass the signal through to line-out). Sure, you won't get to use the front ports this way, but that's no different from what you would have got with the add-in card.
To repair the problem itself
Pulling this off will require you to be able to both solder and desolder double-sided PCBs, and probably also to have an engraver to modify the PCB itself — but if you succeed, it will definitely be worth it. First of all, if the front audio cable that originally came with the case was unshielded, you will need (if you use the microphone jack, at least, but it doesn't hurt to use the shielded cable as a matter of principle) to either assemble a shielded replacement from the parts, or salvage a shielded cable from another case that can be adapted to match the wiring of the subject (I imagine most of us will take the latter, easier way out). Over on the front connector board, you will probably have to desolder the ports themselves, remove them, and then reinstall them after the mod (and make sure not to mix up the headphone and microphone ports if they are indeed colour-coded

So now you know why the expansion sound cards want nothing to do with the front audio ports. It would really be a trivial expense (i.e. the cost of shielded cable, a small resistor, and a ceramic capacitor) on the case manufacturers' part to make all the difference between unusable and perfect front audio, but in this sorry age of penny-pinching, some of them just don't seem to care.

For what it's worth, I have yet to notice the functional limitations of the sound chip on even this 8+-year-old board — most recordings have higher background noise anyway (yep, there's a statement swap, with the new statement being unequivocally true) — so the only reason I could justify an expansion sound card for my own use is if I run out of channels on the integrated version (which I don't see happening any time soon, as I'm currently using headphones for my main listening expectations). (Another statement swap here, as headphones are supposed to have HF roll-off and the treble boosting I set on the EQ for some months was really just giving me headaches.) The days when discrete sound cards were a necessity outside of professional audio and hardcore gaming are long gone indeed.
(Never mind the statement that was originally here; the transition from terrible monitor-integrated speakers just threw off my judgement. Another issue did crop up in the interim, though: The line-in on the Intel D945GTP picks up noise apparently from some other part of the board unless short-circuited. The Gigabyte H87M-D3H doesn't have that problem — not audibly, anyway; any frequency peaks can only be detected with a frequency analyser, and even then are all less than 15dB above the median — so I can only conclude that Intel's mainboard designers just suck. At least, that's one thing I do agree with Topcat on. Anyway, I understand now that 32Ω (let alone the output impedance of the headphone driver) is too low to really be audibly affected by (normal levels of) EMI, and only suffers from the earth loop part. EMI would still attack the front microphone input if the cable is unshielded, of course.
Another thing I found out is that size does matter for coupling capacitors, particularly with 32Ω headphones. Yes, you can compensate with the EQ, but it would be preferable if users didn't have to have electronics knowledge to get the desired bass response.