My audio port is broken. Can I connect audio with a USB device?

My son broke a speaker connection and it is stuck in his audio port. Apple says it can't come out and the entire logic board has to be replaced to the tune of $400.

I was told that i can buy a USB device that will allow him to connect his headphones to his computer and have audio.

Can anyone tell me what i need to buy? I tried one that was $1.15 called a USB External Sound Card, but it does not work.