That is an old ass version of pulse.
The speaker may or may not be fucked but I'm pretty sure a more recent version of pulse would give you more options. It's only relatively recently that pulse actually started being good. I'm on shitty onboard sound so I don't think that's the issue ... although maybe, I don't know much about how sound works.
I don't think there not being 2.1 would be an issue. Analog 2.1 still just uses a standard stereo R/L signal. So you'd hear it through both speakers. Swapping channels of the speakers would tell you if it's a channel issue.
If you can plug in any old spare speaker in its place, I'd give that a go.
Dodgy contacts, joints and leads sounds more likely.
Yeah, I'll have to decide whether this worth repairing, or just wait for another $25 refurb. to come up... I guess it might be worth a $5 + 5-minute gamble.