I have a Dell Inspiron 530s. It has this weird thing that it does, It was broken because it would not power up. So I decided to test the PSU and it worked, only with certain things. My DVD drive was one and the PSU fan also worked and the Harddrive when I tested my PSU with a paperclip and the green and black ground wires. But, after taking it out and I plugged it back in the 24 pin connector, the fans work but not the DVD drive. Here is a video of me showing you. Suggestions on how to fix this would be great.
I believe your problem is the power supply itself, I bet its an old power supply or its just a really bad one. Either way if its an old power supply then the reason would be the capacitors aging so the power supply loses its initial wattage and right now its unable to power on all the devices. Or if its a new power supply then there is not enough watts on it to support your computer.
I think you may have a bit of a problem finding power supplies for that as I believe it uses TFX12v form factor. Verify that the power supply in the link has the same screw slot and is identical. Your power supply factor is quite expensive compared to the normal ATX format.