I do not recommend the oven trick except maybe as an absolute last resort.
It makes things worse more often than it fixes anything and there is a lot you can do before taking that risk.
If it goes badly caps can pop or SMD components can shift. That won't be helpfull.
Capacitors were lightly mentioned.
Those might not be it but they are one of the prime suspects.
Only some bad caps show any outward signs.
Past 15 years old Al-Lytics hit the right end of the bathtub curve.
(Meaning at 15 years the failure starts going up exponentially with time.)
Problems that don't make any sense often turn out to be bad caps.
PcChips tended to use cheap ones.
The little ones (under 6mm) don't fail as often but they do fail too.
A little one related to the chipset or PCI bus timing could take all the slots out.
Here is a direction to start.
As your entire PCI bus is out, do some circuit tracing and find any caps (or SMD parts) that go to all the slots.
Focus on those.
Look at the 32-bit PCI slot pinout and check that all the power voltages are present in the slots.
If not then trace it back to the regulator (or power pin/source) associated with that voltage and check the related components.
Here https://allpinouts.org/pinouts/connectors/buses/pci/
I can't be here much but there are a lot of good techs here to help.
Good luck.
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GRUMPY OLD FART - On Hiatus, sort'a
Mann-Made Global Warming. - We should be more concerned about the Intellectual Climate.
You can teach a man to fish and feed him for life, but if he can't handle sushi you must also teach him to cook.
