[strike]This is because Windows is trying to load the drivers for your storage controller in AHCI mode when it is in compatible mode. This should normally work, but unless you have a specific reason for using compatibility mode, I'd recommend moving back to AHCI mode. It provides better functionality and should resolve your issue.[/strike]
Sorry, I misread your post. If the computer is just not starting up at all, it is most likely because of a power issue: either a bad battery or charger. If you know those aren't the case, then your BIOS may have become messed up and needs to be reset to defaults. There is very little chance that changing your SATA controller mode could brick your computer. And when I say very little, I mean it might as well not exist.