Hi
"How would one go about looking for the issue? Could it be bad electrolytic capacitors (i cant see any problems in terms of looks), corrupted storage/flash? Corrupted RAM chip?"
I doubt it will be the capacitors!
Does the PC boots OK without the sound card ?
Are there any other PCIe cards in the PC ?
Can you try the sound card in another PC ?
(Does it install and work OK)
If so, then the problem is on your PC. It is either the drivers or the PCIe slot (or may even be the whole PCIe system).
Try the sound card in another PCIe slot. If you still have the same locking up problem, uninstall the driver.
You WILL have to delete the driver files for the sound card from the \Windows32 directory, search for how to do this.
The Windows un-install driver does not delete the driver, just disables it!
Re-install the driver.
If that does not work, then Either the card is broken or your PCIe in your PC is broken.