We might need to know more about your setup, but generalizing below... static is caused by one of two things.
1) Excessive ground current in the computer, is something onboard analog audio has trouble rejecting. Sometimes a sound card can help, other times a different PSU helps (less).
2) Poor mechanical connection, like the analog out 3.5mm jack on the motherboard getting loose, or connection at the amp, or amp to speaker terminals. I guess we can rule out the motherboard rear jack since you tried a USB sound card.
Since it's still present with the USB sound card, we "should be" able to rule out the motherboard, maybe still the PSU so you could try an alternate power source/injector for the USB sound card, or if the motherboard has jumpers or bios selection for whether USB runs off main 5V PSU rail vs 5VSB rail, try toggling that.
Another option if you have digital out, or a sound card with that feature is digital out, then the amp, so you avoid having the sound device itself being both the analog out and powered by the computer PSU.
One last thing to consider is if the USB port is powered by 5VSB and you can't change that, it's possible your PSU is starting to have the capacitor(s) on the 5VSB circuit fail. This is common with low end PSU but also those that have long off periods, where they still are powering connected devices but no fan running so that subcircuit of the PSU stays hotter and wears faster... takes a combination of factors to happen, but if the PSU is due to have dust cleaned out anyway then I'd take a look at the caps to see if any are vented.
As far as replacing the motherboard, differences in design can change where the ground current ripple is so it is possible that would help, but I'd as soon try a sound card instead, has just as much of a potential to fix it as a new motherboard does if none of the above helps.
Lastly as with different mobos having different ground current at different spots, different USB ports can too so if you haven't, try the USB sound on a different USB port, especially front vs rear port.