Your board (kind of an old momma) only has standard PCI slot interfaces, not PCI-E slots. These two interfaces are mechanically and functionally incompatible. So not only will a PCI-E card not fit in a PCI slot, the protocol of these interfaces is completely different, so it would not work even if it fit.
This is the Product Guide for your board:
According to this document, only standard PCI slots are used on this board.
I did find one PCI to USB 3.0 interface card at an E-tailer, but it sure isn't cheap, as much as a cheap mother board.
If your new card is for use with a PCI-E slot, it won't work. I found one mother board on the same E-tailer as the PCI to USB 3.0 card, for socket 478 CPUs, which did have one PCI-E slot, but no USB 3.0 ports.
It's great that this seven or eight year old PC is still cycling along, but PC years are like dog years, it might be time to retire that momma, sorry to say.