NVidia (GTX 680) Drivers Ubuntu 13.04 Black Screen

I've been trying for two days now to get my computer running the NVidia drivers. I'm running a GTX 680 and 64 bit architecture.

I've tried multiple things, here's a few:

The Additional Drivers tab shows nothing, but I have used sudo apt-get install nvidia-current and pretty much every other nvidia package I could find using apt-cache search nvidia

I've downloaded the .run file from NVidia's website, and logged out, started a VTY session, stopped lightdm, installed it, and rebooted, multiple times.

No matter the approach, the outcome seems to be the same. The system boots, I can hear the splash screen, where I am supposed to log in, but the screen is black, and backlight is off. I can't get into any VTY session like that, I have to reboot and add nomodeset to the boot options. I still get a black screen when I let it go to the login screen, but I can get in a VTY session. Regardless, I have yet to be able to fix it.

Edit 1

Not sure of the importance, but I am running a 2560x1600 native resolution monitor, if that somehow plays into it at all.

The NVIDIA card is connected to a 27" monitor made by Catleap. It doesn't communicate it's capabilities well through EDID, and xserver can't work out what resolution and refresh rate to use. The following xorg.conf solves the problem:

# nvidia-xconfig: X configuration file generated by nvidia-xconfig
# nvidia-xconfig:  version 313.30  (buildmeister@swio-display-x86-rhel47-05)  Wed Mar 27 16:37:22 PDT 2013

Section "ServerLayout"
    Identifier     "Layout0"
    Screen      0  "Screen0"
    InputDevice    "Keyboard0" "CoreKeyboard"
    InputDevice    "Mouse0" "CorePointer"
EndSection


Section "Files"
EndSection

Section "InputDevice"
    # generated from default
    Identifier     "Mouse0"
    Driver         "mouse"
    Option         "Protocol" "auto"
    Option         "Device" "/dev/psaux"
    Option         "Emulate3Buttons" "no"

    Option         "ZAxisMapping" "4 5"
EndSection

Section "InputDevice"
    # generated from default
    Identifier     "Keyboard0"
    Driver         "kbd"
EndSection

Section "Monitor"

    Identifier     "Monitor0"
    VendorName     "Unknown"
    ModelName      "Unknown"
    HorizSync       88.8
    VertRefresh     59.5
    Option         "DPMS"
    Modeline       "2560x1440_60.00" 241.50 2560 2608 2640 2720 1440 1443 1448 1481 +HSync -VSync
    DisplaySize    597 336
EndSection


Section "Device"
    Identifier     "Device0"
    Driver         "nvidia"
    VendorName     "NVIDIA Corporation"
EndSection

Section "Screen"
    Identifier     "Screen0"
    Device         "Device0"
    Monitor        "Monitor0"

    DefaultDepth    24
    Option         "NoLogo" "True"
    Option         "UseEDID" "False"
    Option         "UseEDIDDPI" "False"
    Option         "UseEDIDFreqs" "False"
    Option         "ExactModeTimingsDVI" "True"
    Option         "metamodes" "2560x1440_60 +0 +0"
    SubSection     "Display"
        Depth       24
    EndSubSection

EndSection