So, I just installed my EVGA 1070 FTW today, upgraded from a venerable EVGA 660ti.  The new card is beautiful to behold.
My machine is built on an EVGA X58 mobo with 6GB of RAM and a core i7 920.
I followed the steps from this thread (parts 1 and 2, clean boot, DDU, etc.) -- as for #3, I don't suppose I can use the Nvidia Control Panel if I don't have any graphics drivers installed?

I've tried drivers 368.39, 368.69, 368.81 and the hotfix 368.95.
I get Driver Failed to Install each time.   Here's the tail (with faults) from my machine's setupapi.app.log :
 
>>> [SetupUninstallOEMInf - oem4.inf]
>>> Section start 2016/08/01 23:04:51.390
cmd: C:\Windows\system32\RunDll32.EXE "C:\Program Files\NVIDIA Corporation\Installer2\CoreTemp.{B2AB6BC4-9CDC-48F9-9E62-CA414A42AC0B}\NVPrxy64.DLL",Proxy {FE77E8EB-DAEE-412B-80E1-B5D13105B9A0}
sto: {Delete Driver Package: C:\Windows\System32\DriverStore\FileRepository\nv_dispi.inf_amd64_neutral_0ad8f1f98b4ad733\nv_dispi.inf} 23:04:51.422
sto: Deleting driver package from Driver Store:
sto: Driver Store = C:\Windows\System32\DriverStore (Online | 6.1.7601)
sto: Driver Package = C:\Windows\System32\DriverStore\FileRepository\nv_dispi.inf_amd64_neutral_0ad8f1f98b4ad733\nv_dispi.inf
sto: Flags = 0x00000000
pol: {Driver package policy check} 23:04:51.422
pol: {Driver package policy check - exit(0x00000000)} 23:04:51.422
sto: {Unstage Driver Package: C:\Windows\System32\DriverStore\FileRepository\nv_dispi.inf_amd64_neutral_0ad8f1f98b4ad733\nv_dispi.inf} 23:04:51.422
sto: Published driver package INF 'oem4.inf' was deleted.
sto: {Delete Directory: C:\Windows\System32\DriverStore\FileRepository\nv_dispi.inf_amd64_neutral_0ad8f1f98b4ad733} 23:04:51.718
sto: {Delete Directory: exit(0x00000000)} 23:04:51.765
sto: {Unstage Driver Package: exit(0x00000000)} 23:04:51.765
sto: Deleted driver package from Driver Store. Time = 343 ms
sto: {Delete Driver Package: exit(0x00000000)} 23:04:51.765
<<< Section end 2016/08/01 23:04:53.372
<<< [Exit status: SUCCESS]
 
! dvi: Installing NULL driver!
! dvi: Failed to set Device Description property: (null)
! dvi: Error 1784: The supplied user buffer is not valid for the requested operation.
 
 
Thanks!  I've been at this all evening, hoping to enjoy my early birthday gift.  :)
 
 

I just flashed my mobo BIOS to the last released version, reset all of the settings in BIOS to default, and repeated the DDU in safe mode step on a clean boot, and yes, tried to install the latest driver (and some previous ones) as Administrator.  
 
Thanks for the tip, but sadly, no dice.  Installations Fail out and log the same error logged as before.
 

I wonder if having more Vram than System ram might be a problem? I recall something about then requiring 24 GB of ram for the titan black that had 12 GB of Vram, I'm trying to find a list of system requirements atm....

Thanks for the tips, guys!  
 
My Motherboard is a few years old now, and it only has BIOS, not UEFI, so there isn't a Legacy mode to enable (unless I just do not understand the question?).
 
I uninstalled the A/V (no change), but the driver download refuses to run install in Safe Mode altogether.  I'll try booting to Safe Mode with networking and using Device Manager to update the driver.
 
I've never heard of a conflict between system memory and VRAM on a discrete card on a 64-bit System.  I know the old 32-bit OS's run out of address space around 4GB total, but that's not the case here.  Almost everyone else, it seems, is running this card is on Windows 10, but I like 7 and the free upgrade period for Win10 expired a couple of days ago.
 

You may need to change the Memory Low Gap setting to 3G. See THIS FAQ for instructions for doing so; you may be correct that it's a system memory vs VRAM problem, assuming you're using the EVGA x58 in your sig. 

Cool GTX
If your MB drivers & Win 7 SP1 security updates are current, Then:
 
Close ALL background software
(unplug - go off line for security, cause your security software should be OFF - not removed)
 
Open Device Manager
select Display adapter
Select your GPU
Right click GPU
Chose uninstall
Scan for hardware changes
install driver
  
System details are always helpful
 

Thanks, Cool GTX!!
 
Part of my confusion was that "Display Adapter" didn't appear in my Device Manager at all, just (?) HD Audio and  a pair of (?) Other entries.  
 
Hosing those and letting Windows install the driver seems to have worked!  After deleting them and scanning for new hardware, the DM showed me (?) VGA Compatible Adapter instead of just (?) Other.  I rebooted and let Windows update the driver, and now it says I have 368.39 installed!
 
I'm going to reboot and try out a game with this driver; now that my Device Manager issue is solved, do you think it is safe to update to the latest release driver from Nvidia?  (368.81)