Yes, really strange. But a PCIe card should work. However, I wouldn't guarantee that you can boot from it – you should be able to though.
But try resetting the CMOS first. If that doesn't work, update the BIOS if you can.
Thanks for the suggestion. I removed and inserted the CMOS battery (couldn't find a jumper), to no effect (drives still not detected by BIOS). I'll look into doing a BIOS update.