I had a similar issue with a Powercolor graphics card and I could not get it to work no matter what I tried. I ended up having to take a loss and send the card back to Newegg because of compatibility issues and took a $20 dollar shipping loss and $20 dollar restocking fee to send it back.
On some of the newer Dell Optiplex models I have to work with it seems that there are a lot of problems getting dual monitors to setup and work properly with both on-board video and the dedicated PCI-E video card. You should have your BIOS setup as it is to "PCI-E Express card" or "preferred / auto" if you cannot disable on-board video. The BIOS I have would let you choose PCI-E External (PEG), PCI-E (INT), and Auto. If you can set it to auto or not I am not sure but I do know that if you remove the power cable from the power supply and disconnect all your video cables from your computer and then plug in the video cable to the PCI-E card and not the on-board video and plug the power back in that it should power on just for a second to detect the video.
If it does not power on for a second when you plug the power cable back into the PSU I would try unplugging the power again, removing the CMOS battery for 15 minutes or so and plug your Powercolor graphics card back into the PCI-E slot, connect the video cable to that card and not to onboard video, plug the CMOS battery back in and then plug the power back into your PSU. You should see some kind of activity like the CPU Fan spinning up like your PC is powering on for a second and it will shut back off (I think this is for it to detect what video is attached) from what I have seen and experienced.
The problem with my power color card was that apparently it did not like the motherboard which was an Intel based motherboard, and I am not sure why since everything is supposed to be "backward compatible" with PCI-E and I have found that for some motherboards it is not.
I could not determine if this was due to the UEFI BIOS ready setup or not but I do know that with the way Windows was installed on the box that I have it was set natively to RAID and not ACHI, and I believe something was screwing it up during boot with the Video BIOS which was UEFI Ready. I could get a display and it would say "A bootable device has not been detected.rom the FV] Please refer to the Product Guide at http://support(dot)intel(dot)com/support/motherboards/desktop.
The only way I could even get this to display during boot was to use the DVI > VGA adapter that came with the card and connect it to the VGA cable which then plugged into my 24" HD display's VGA port.
I will post something else to see if anyone has any suggestions to a fix for that but that is really all I can offer you. My symptoms were similar to yours, no matter what kind of cable I used (HDMI, DVI, Display Port) all would boot up with a blank screen for some time and eventually go to "no signal". I hope what I have offered here helps you out somewhat but it is possible if your BIOS is setup like mine was when Windows was installed it may be doing the same thing. I am not sure if it is due to the Native RAID setup in BIOS or the Video card's UEFI Ready BIOS. I was not able to get it to work period even unplugging all my hard drives and attempting to boot from Ubuntu in a live-cd environment.
Good luck.