|"I have a power supply tester, and found everything to be within normal range"|
PSU testers are fairly useless. All it does is verify voltage, not amperage. And if the PSU is putting out enough amperage, the system will not boot.
You don't need a HDD to get a display. If you're not getting the initial POST beep, the problem is either the CPU or motherboard, possibly the PSU. I would remove/disconnect all non-essential hardware to try to bring up the POST screen. Unplug the HDD, optical drive, floppy drive, remove all cards, remove all RAM but one stick, unplug all external devices except the keyboard & monitor....then try to boot up. If there's still no display, clear CMOS & try again.