I just built a new computer (my first) in a Nine Hundred case. The front panel audio is very noisy, and I think it's because of the extraneous AC97 connector hanging off the Intel one, which seems to be acting as an antenna. Can I safely cut this off? Should I just wrap it up in some insulating tape or something? Can I ground it? It's very frustrating, and I didn't have this problem on my old computer (A Dell from 2002.)

Your question isn't very clear. You are assumming we will have a personal knowledge of this particular case. If you elaborate on what the actual problem is, someone will attempt to help.

There is an intel hd audio connector attached to my sound card, and hanging off of that is an extraneous AC'97 connector. The wires connecting the two are not well insulated, and there's lots of noise when I plug in my headphones.

See picture for details. http://bayimg.com/eAGbiAABf

Can I safely cut off this AC'97 connector or will that break things? Can I insulate it?

Are you sure that isn't a cable that is plugged into a header. That cable isn't in use? What connects the headphone jack to the card? That would be the place to look. If a signal isn't traveling thru a cable it would be less likely to pick up stray noise than one that is carrying a signal.

The cable has two dongles on it, one for the Intel HD audio pins and one for the AC'97 audio pins, like this:

[front panel]==============[intel]----[ac97]

The intel dongle is attached to my card. The ac97 one is there if you have a sound card with those front panel pins. For me, it just hangs there, and the wires aren't well insulated, which is why I think it's picking up noise. I could be wrong, though. In any case the front panel headphone jack is very noisy, and the jacks in the back of the card are not, which is why I suspect the wire.

But the cable you want to deal with isn't the cable carrying the signal to the front jack, is it? That is the cable to shield. Sometimes just separating from other cables is enough.

I understand what you are suggesting about the AC97 cable acting like an antenna and possibly picking up RF noise. I guess that's possible. If there's no chance of ever having to use it, I don't see any problem with cutting it off. If you want to make sure that it's the problem, you could wrap it with tinfoil. But make sure it's insulated and/or kept away from any contact with electrical components during the test. Grounding it is not a good idea! (edit) That is unless you determine a ground line in the cable and ground it, that 'might' help.