Possible causes of "streaks" on LCD monitor

"I would check the cable & connection first. Can you switch cables/monitors so the inky display is using the DVI and vice versa? If so, we could potentially rule out a monitor issue.

My experience says this kind of problem would be the cable connection first, then card, then monitor.

If it's the connection, re-seating the cable may fix the issue.
If not, try replacing the cable. Since the problem only after some time, I think it's probably not the cable itself.
If that doesn't help, check the card, is the fan working? Long shot, but it could be a heat issue.

One of those DVI-to-VGA adapters might be helpful for troubleshooting. Switching monitors/ports/cables would definitely be a big help in narrowing down the issue.

Let's say we have Monitor A with Cable A on Port A (DVI)
And Monitor B with Cable B on Port B (VGA)

1) Try Monitor A with Cable B on Port B and Monitor B with Cable A on Port A

If Monitor A exhibits the issue, you know the monitors are not the problem.
If Monitor B exhibits the issue, you know that Monitor B is the problem.

If the monitors are not the problem.....

2) Try Monitor A with Cable A on Port B and Monitor B with Cable B on Port A

If Monitor A exhibits the issue, you know the card is the problem.
If Monitor B exhibits the issue, you know the B cable is the problem."