Computer audio problem: Is it my speakers or my computer?

My computer keeps telling me that the speakers aren’t plugged in, but they are. It happens periodically, not constantly. I fiddle with the connection, and it doesn’t fix the problem. It seems to just go away on its own, only to come back later.

How can I tell if the problem is with the speakers (the cord?) or the speaker port on the computer or the computer itself? I’d hate to have to buy new speakers only to find it doesn’t correct the issue. Not to mention, there is NO money in the budget to fix this issue.