If there's absolutely no problem, that suggests one of two things:
A grounding problem (like kevh suggested above) - if there's a short circuit, like the PCB touching the case, then no power will get to any of the components, and nothing will happen.
Alternatively, you've not wired up the front panel correctly. In an Amiga, the power switch is connected to the PSU directly, but in an ATX system, the PSU gets its power switch from the motherboard, which in turn is connected to the front panel. In fact the motherboard always has power, and tells the PSU when to supply the other power connectors. Hence if the front panel switch isn't connected to the motherboard correctly, then pressing the front switch won't be telling the motherboard to supply power to anything else (including the disks). This is probably your problem, as even a knackered motherboard will usually be able to signal the PSU to power up when the switch is pressed.
Good luck!
