This is highly variable depending on what you're using and the precise implementation. You might find that a 3 dollar USB dongle is good enough or that the nice expensive 'audiophile' DAC you bought is crap.
Lets start with the obvious - USB sound cards are perfectly safe. Some audiophiles prefer them cause they supposedly isolate the sound circuits from the main system so 'they sound better'. There's no inherent risk to a USB sound card - I've run (granted, a high quality) USB powered sound card for years and not come across any issues.
As for USB versus onboard - these days, with commodity systems having on board sound, the budget sound card is dead. Most sound cards try to offer you something beyond basic sound features. If you want a sound card to troubleshoot a usb sound card is a better choice. If you want additional features, then look at on board cards.
All that said, I'd test my whole sound chain - if you're using speakers, see if you can plug in a (cheap) pair of headphones to the back panel to see if thats the problem.If so, I'd try swapping cables on the speakers to rule that out too. I'd also try a linux live cd to rule out the sound card. I'd look at the volume meter in the mixer on windows 7 or better to make sure you just don't have low volume. Sound cards dying is kind of irregular. No point replacing your sound card, if your speakers are at fault.
If it is your sound card start looking at your needs, whether you are alright with the extra mess of a USB sound card, or if you can find a internal card that meets your price/requirements and you'll be on your way. The big things to look at really are outputs and inputs, if you arn't a massive audiophile. Nearly modern card will output to a single pair of speakers, and I wouldn't recommend going for something fancy if thats all you need.