What motherboard are you running? and have you tried updating the drivers for it? I ask because both cards that have not worked push a lot more data than the 8600 so I am wondering if maybe your mobo drivers are either out of date of corrupt. It's an outside chance but an easy try.
I am also wondering if maybe the PCI-E lanes may be compromised somehow, either by way of a partial short or thermal damage. Again, very slim chance but it does fit the symptoms.
As a recap, uninstall all graphics drivers through the Add/Remove Programs in Windows, boot to safe mode, run DriverSweeper, have it clean out any graphics drivers (Nvidia and ATI), reboot into Windows, then try installing the drivers for whichever card you want to run.
Also, try using CCleaner to lasso in your background apps that launch with Windows. This could all be some kind of resource clash.