On a 7- or 8-year-old computer it's probably not worth bothering with. Generally when I see someone ride out the same machine that long, they tend to be entry-level boxes to begin with. Even if you bought a high-end set up from that era
like this $3,600 job circa 2004, it would hold virtually no resale value today. So the overwhelmingly likely answer to what you should do with it is just dispose of it. Maybe find a leftover IDE-style used hard drive and put an OS on it to give to a kid if you want.
The good news is that basically any off-the-shelf desktop will do what you want, you just might have to stick in a couple cheap video cards to run 4 displays. So something with two PCI-E ports internally would do the trick. Installing two simple video cards is pretty straightforward for a novice DIY'er, just need a phillips head screwdriver and the ability to slide a card into a slot.
What specific cards you'd want depends on the monitors' connectivity. If you're rocking 4 old school displays figure out if they have VGA or DVI connections or what. You can look those up and know the difference quickly. Fwiw, VGA is almost obsolete and DVI isn't that far behind, though still common presently. You can still find low-cost basic cards with what you need today. Given the choice, try to avoid using VGA connections if you can.
Overall there's been a ton of evolution in desktop PCs and displays since you last bought one, so there's a huge benefit to just replacing it. A $500 machine (tops) will generally come with a basic mouse and keyboard, and the added cards your 4 displays require might go another $80. If you were content with two monitors you wouldn't need even the cards in favor of just the built-in video.