You mean 1080p?
No. I mean
1080i. This appears to be what the cameras use, and it's somewhat uncommon these days, so some devices may not support it.
However, AFAIK people who had problems with this in the past didn't have the same problem you're having now. They reported the camera falling back to 720x480, and I would generally expect the camera to recognize the connection even if this problem was present.
So you think there's an issue with the video capture card?
The normal behavior of these cameras is to turn off the display when an HDMI connection is detected.
This is described in the camera manual (page 150, on the version I have) "Images from the camera are now displayed on the TV. (Nothing is displayed on the camera screen.)"
So the fact it's not doing that means it isn't sensing the HDMI connection. This could be a physical connection problem (in the camera, the cabling, or the device) or some other defect or incompatiblity.
The vertical lines suggest your capture device is talking to your computer, but not seeing signal, which makes sense, because the camera won't produce output on the HDMI port unless it thinks something is there.
The most straightforward way to narrow down where the problem is would be to try the various components with other devices.
If you have another device capable of displaying HDMI (a monitor or TV with HDMI input) you try connecting the the camera to that, assuming you have the correct adapters. You can also connect the camera to a DVI monitor if you have and HDMI to DVI adapter.