The computer looks like 2000-2001ish with little in terms of yellowing, so early-mid 2000s would be my guess.
The satellite to the right of the monitor belongs to a Cambridge Soundworks system that was made in 2.1 and 4.1 varieties and was quite popular in 1999-2000, had one at the computer myself (if the fuzzy grey matter storage does not deceive me, original price for the 2.1 149 DM and later reduced to 99 DM around here, which I though was a great deal back then). 2.5" satellites, 5" 'sub', all plastic but actually quite robust. I later figured out that placing the 'sublet' next to the satellites instead of under the desk and stuffing the port with an old sock actually gave pretty good sound. Was my bedside setup for years. (My parents got a slightly later version with larger satellites, never liked that one very much.) A while back I actually picked up a used set in good condition on eBay for a musically inclined (and rather severely autistic) colleague who wanted decent sound at his office PC for not a lot of money, and he was over the moon with the sound quality.
While the OP seems to have left for now, another possible solution I can think of would involve an older (let's say 10-year-old) business laptop with a decent built-in optical drive and acceptable noise levels that could be used for ripping, building a digital collection and being the centerpiece of a playback setup. (Dell E6x20/30 series, Thinkpad Tx20/30, something like that. I also like the T510 but those seem to be plagued with bad sound chips. Their screens generally kind of suck, but in a music player who really cares. I may be able to help out with a matching ICC profile, not sure whether there is any quicker method for determining the panel type than installing DisplayCAL though.) In the 'States, picking up a decent machine for less than 100 bucks should be quite feasible. I would throw out the old harddrive for a decent 2.5" SSD though, WD Blue / Sandisk Ultra 3D or Crucial MX500 is what I typically go with these days (splurge on 500 gigs if money allows; the WD / Sandisk are faster in small sizes but may be prone to reliability issues in the larger ones, so for 250s I generally buy WD / Sandisk, 500s could be either, and MX500 for 1 TB).
I actually set up some Edifier 1280Ts recently. Bass / treble ca. -2 for both. Not the cleanest highs I've heard (and the vertical is expectedly uneven, even after a bit of raise from the desk with small boxes for makeshift stands) but overall pretty good, they really go quite loud too. For multimedia speakers, they're fine. When you've got serious hi-fi ambitions, I'd rather be looking at accommodating some JBL 305s, Adam T5Vs, Kali LP6s or the like.