How to Get a good connection to a Regular Amp with RCA plugs

The Behringer is for inputting audio, not output.

I've never really run across any problems with audio jacks on PC's. Obviously there can be problems, but very rarely. I don't have any problems with the plugs either. There are gold plated connectors, but unless both the jack and plug are gold it isn't worth the extra cost for just gold plated plugs.

One other possibility is a "ground loop" problem - a difference in electronic potential of the grounds in two devices. One thing to try is "lift" the ground on the amplifier AC power plug (if its a 3 prong plug). You can get an adapter for the AC power plug. We run into ground loop problems (hum) quite frequently with AC powered musical equipment.

As I previously mentioned, if you have S/PDIF (digital) output on the PC and an S/PDIF input on the amplifier consider using this instead of the analog audio connections.

Hum well I agree with fireberd the likelihood of the board socket being broken or faulty is highly unlikely but it doesn't rule out that one use has dislodged a potential dry joint and that the jack it self was perhaps faulty / weak at manufacture.
As suggested try another lead, and if necessary use an old one with stripped ends to carefully test for continuity in right / left and ground leads (socket to lead end) . .

Just an update; I got a new cable from my dad the other night and a new amp. I've only hooked up the cable so far. I've played a fair amount of music the last couple days and it has all sounded perfect.

This is now the 4th new cable I've tried. So I'll give it a little more time before I say for sure that this cable fixed it. If I have more problems, I'm ready to swap out the amp with a different one.

Thanks,
Jamie

Well done Jamie and just for the record mate always buy good quality leads some of the rubbish that you think is a bargain is really - well rubbish.

Another good thing to do if you are using that jack a lot is to reinforce the lead from the jack to about two inches out with some of that cloth duct tape - doesn't need to look glamorous and in most cases i don't even notice it. Its just there where a lot of flex takes place mate.