New Power Supply Won't Work in Inspiron 620 (Old PSU works fine)

I have an Inspiron 620 and I want to upgrade the PSU so that I can install a better graphics card. The stock PSU is only 300W and doesn't have a 6-pin connector.

I've tried three new PSUs, and none of them will get it running. I connect power and the orange light on the board lights up, just like it does with the old supply. But, the power switch doesn't light up, and pressing it does absolutely nothing.

I jumped the green pin on the board connector and that fired up the fans, but it doesn't post. The power button light will come on now, too, but I get no beep, no usb power, no video. If I put in a drive, it spins up the drive. 

If I put the original 300W supply back in, it boots just fine. 

I've read many reports that any ATX PSU should work. I did read one forum where a dell guy said only 300W PSUs will work, but I've seen reports to the contrary. Is there any possibility that the PSUs I tried are incompatible? One is an EarthWatts 650, and I've tried 2 new Thermaltake 600 TR2s. I may try a Corsair or EVGA if it's likely to make a difference.

Is there a chance that something is wrong with my motherboard? I don't understand why it works with the 300 but not a 600.

Thank you for any suggestions.