I can switch the RCA-cable's jack plugs around, and as a result the right speaker starts working again but the left one goes mute instead. When I play CDs both speakers are working, as they are when I'm playing something on a mp3 player using the same cable. So looks like neither the speakers nor the cable are the culprits here. With headphones connected to the laptop everything works just fine too. But here's the weird part: when I unplug the power cord from the computer, both speakers start working.
I updated the sound card drivers (the card is integrated I guess, it's called "Realtek HD Audio" if it's any help) but nothing changed. I could use some help, I'm completely clueless about this.