I've never owned a DFI socket 370 board so I'm not sure how good it is but I had a few DFI boards for AMD Athlons that I liked. That's not really enough info to tell you much I know...

Are the smaller caps Nichicon? Black and white/silvery-white is a common color but if it's a better brand than Teapo, they're more likely OK (note that I said 'more likely', not 'more than likely'). I would advise replacing any of them that were near any component that might have gotten hot if you don't want to replace all of them. Those caps will be super cheap, though, if you get them from a site like Mouser or Digikey or Farnell or something like that where you can get small caps from decent brands for maybe 10-20 cents each (plus a small amount of shipping). Those larger caps might cost you 30-50 cents each or you could go for solid aka aluminum polymer caps which are physically smaller and handle about twice the ripple current, and those'll cost around 50-75 cents each.

It's not just that using a bad brand like Teapo will cause problems; it's that bad caps like Teapo don't hold up to temperature. Usually they'll go bad when they are near heatsinks that get hot, so always make sure case airflow is good, and don't obsess over your computer having a little bit of fan noise by going passive. You'll kill the capacitors by your video card (and maybe elsewhere) from the heat. Heck this board probably had a fan on the CPU heatsink and still got too hot in the area (make sure to use a better heatsink and fan than the previous owner).

Personally I do think recapping is usually a good way to go because, frankly, there's a poor selection of this equipment for sale these days and I like saving equipment and keeping it going. Maybe someday it will wind up in the hands of someone much younger than me who may be interested in the same retro games. And I'd rather send a handful of capacitors to the landfill than an entire PCB (and yes you can "recycle" PCBs, but that actually just means they get put in a landfill in China instead.)

Actually this board never got any heat outside of the factory since the box was still sealed when I got it, as I mentioned it's new old stock. So, the capacitors failed while the board was still in storage (which is not surprising, I've seen the same thing happening with power supplies from that era).

Unfortunately the smaller 10uf capacitors are also Teapo, maybe I will get replacements for those next time I order something from Mouser.

Wow. That's pretty bad. I've had Teapos go on Abit boards and such but those boards were well-used. I would also say ripple current could also kill them, but that's of course another thing they won't see while sitting in the box. These caps are even worse than I thought! Geez!

They're 15 year old caps. That's well beyond the nominal lifetime for most capacitors under normal usage. Yes, the caps failing in storage is somewhat strange, but caps do have a lifetime under no load, and we don't know what the storage conditions were (what were the temperature ranges and cycling conditions).

For that matter, it might have been used and resealed then sold as NOS. Some people are pretty good at rewrapping.

Teapos are far from the worst capacitors (although I haven't heard anything positive of their low ESR caps). For the absolute worst, you have to look at companies like Fuhjyyu and Chhsi or the illegal knockoff lines.