At a guess, your power supply is not distributing any power to the +5VSB rail, the only one to be active when the computer is off. With out that, the computer cannot start up. When in sleep (ACPI S3, Suspend To RAM, what Windows calls Standby and OS X calls Sleep) there is other power on to the motherboard, and so you can start. What Windows calls Hibernate is something else (ACPI S4) that you cannot reach in OS X except by having the machine sleep and then letting the battery run down.
In any case, I think you need to bring the machine in for service or, if you're as comfortable with picking it apart as you seem to be, do some more detailed troubleshooting by opening it up and looking for leaking caps.