Make sure the Reset Switch is connected - IIRC the switch is usually active low, i.e. when there's no connection between the pins, that's a reset signal. No switch = No connection = permanent reset trigger.
At least, that's how I remember it....
You remember wrong.
For what it's worth my A1XE needs to be turned on twice - the first time there's no graphic display or anything (but the CPU fan goes), then I turn it off then on again and it works. It's a bug in the Radeon cards, they need a PCI Reset - happens on a lot of PCs too.
Lacking PCI reset is a bug of the motherboard.