Looks like it doesn't have AHCI! If you absolutely need it, it shouldn't be difficult to find an LGA 775 motherboard with a chipset and BIOS supporting AHCI.
There should be an option for SATA configuration under one of the BIOS menus. On some systems its defaulted to IDE, but select that option and there should be IDE, AHCI, and in most boards, RAID.
Looks like it doesn't have AHCI! If you absolutely need it, it shouldn't be difficult to find an LGA 775 motherboard with a chipset and BIOS supporting AHCI.
Unfortunately it doesn't seem like you can do so. I would contact ASRock and ask them if they've any BIOS updates that would provide this functionality, though they might not. Your best bet would be to, yes, get another LGA775 motherboard.
What exactly are you trying to do that requires AHCI? Hot swapping?