New graphics card(s) not recognized. PCI-e slot dead?

Other stuff I've tried:

Same procedure with onboard graphics not disabled. 

Graphics card driver has been installed and is most up to date version. 

Installed card but connected VGA cable to onboard graphics (get an error message on boot up saying that port has been disabled and won't work)

INTEL Multi Display is available if its not disabled in bios.  Monitors don't work automatic you have to enable them WHILE hooked up. R7 240 does not require a new power supply.  The Dell 305W power supply is EPS12v. Minimum replacement is Corsair CS750M.

$29 Joes crab shack power supplies don't work. ATX is Not sufficient.

You need 20W minimum on the 5VSB rails.  I have an R7 250E and stock power supply with 4GHZ Core I7 and 16 gigs of ram and 4 monitors and it works fine with the stock 305W power supply.

Thanks for the reply. 

FYI, this is the card SAPPHIRE R7 240 2GB DDR3 WITH BOOST. 

It specifies 400w minimum. I assume 600w is not a problem. It is EVGA 600B power supply (better than Joe's Crab shack? :-)  ). 

In the BIOS, Intel Multi Display is an option that is part of the ONBOARD GRAPHICS option. I assumed it only affected onboard graphics vs. a separate graphics card. 

Note: I've disabled Security on boot in the BIOS (suggested elsewhere as a solution). 

I enabled INTEL Multi Display in the BIOS. Reinstalled the card and connected VGA cable to it. Still no signal to the monitor. Then I connected monitors to onboard and the graphics card. It booted!

But on the onboard graphics connected worked. I looked in Device Manager and it had a second display adaptor: Microsoft Basic Display Adaptor. I ran update the driver (even though I had installed the driver without the card installed. 

Now I am getting a checkerboard screen on the card-connected monitor and blank on the onboard connected monitor (but there is a signal). The checkerboard is on for a bit, then off.  Re-booted, no change. 

Disconnected card-connected monitor, Re-booted. 

The R7 showed up as a Display adaptor in Device Manager. I re-installed the driver (directly from the exe file). It ran without errors and it now shows as operating properly in Device Manager. 

Re-booted with card-connected monitor. Blank screen for a while, then the checkerboard pattern. 

Re-installed Catalyst software and it asked me to re-boot (first time it has done that). 

Catalyst Control Centre now shows up a a menu item when I right click on the desktop. Checked driver update and used their driver detect software to pick the right driver. There is a newer driver (mine was from the Sapphire website and was dated Sept 2014). Updated driver. Took quite a bit longer than previously. Re-booting. 

PC really seems to be running slowly.

Disabled onboard grapics through device manager and re-booted with monitor connected to graphics card. More of the checkerboard pattern. 

Re-installed Catalyst software and it asked me to re-boot (first time it has done that). 

Catalyst Control Centre now shows up a a menu item when I right click on the desktop. Checked driver update and used their driver detect software to pick the right driver. There is a newer driver (mine was from the Sapphire website and was dated Sept 2014). Updated driver. Took quite a bit longer than previously. Re-booting. 

PC really seems to be running slowly.

Disabled onboard grapics through device manager and re-booted with monitor connected to graphics card. More of the checkerboard pattern. 

RMA'd the video card and it turns out that I had a bad card. So it looks like all the things I did up to the point where I got a checkerboard pattern worked!