I think the GTX 650 comes with two DVI, an HDMI, and either DisplayPort, or Mini-DisplayPort. HDMI is now capable of up to 4k resolutions (there is some argument about maximum frame rates). Some cables cannot support 4k above 30fps, so you want to look for HDMI 2.0, rather than 1.4 or earlier. DisplayPort 1.2 supports 4k up to 60Hz, but also supports Adaptive Sync. I am fairly sure that NVidia and AMD both support Adaptive Sync now, but so must the monitor. I think HDMI supports GSync, and AMDs FreeSync, but I believe Adaptive Sync is still DisplayPort only, unless there has been a change in the last six months. Both HDMI and DisplayPort support up to 32 channels of audio and 1536kHz sampling rate.
Probably what happened to Dogtown is the card's BIOS locked up the outputs. I don't know why that happened in this case, but I suspect it was connected to a hot device. The card will reset the outputs when it senses a change in cabling.