Check both bios of the card (I assume it has a little dual-bios dip switch, full reboot first, disable HW FastBoot in Bios/Uefi for this just in case as well).
I assume the second monitor you tried had another cable, otherwise check cables - are you using DVI-D?
Maybe check on Techpowerup Firmware Database for newer bios / reflash same one maybe even. http://www.techpowerup.com/vgabios/index.php?architecture=&manufacturer=Sapphire&model=R9+290&interface=&memType=&memSize= . You can use Ati Win Flash, took some 5min, freezes screen and program, so no touching the power button.If anything goes wrong, you got a second bios left anyway.
Check with Hawaii Info / Memory Info (google pls) if you got Hynix or Elpida - or take off cooler to check. Elpida has more black-screen issues. While you are at it, if you open it up, make sure everything is as is should be - and I am not joking unfortunately. Pls check my link below... (i.e. memory getting hot maybe)
DDU in safe mode, run for both nvidia and also amd (twice total),w/o allowing Win to install new ones (little check box), but was already mentioned.
Vertical lines could relate to the gpu or the memory (or many other things like outputs etc pp), although memory usually gives black screen straight away, where gpu gives funny flashes, lines and you name it. It is strange that you experience more issues in Windows than in games though.
Maybe try MSI Afterburner, and just set core at 947 and memory at 1250 (stock reference), see if that makes any difference at all.
If all fails, maybe just DOA ... :(
My Sapphire 290X Tri-X had a broken fan, my replacement Vapor-X has QC issues: https://teksyndicate.com/forum/gpu/sapphire-r9-290x-tri-x-oc-warranty-issue/194025
g/l