That's possible. I've had people send monitors in for service because of lines or distortion, but since the lines don't show up when they print they figure it's the monitor's fault. A new video card fixes that. Or the monitor might be at fault.
Test the monitor with another computer. If you don't have more than one, get a friend to bring over a laptop. Except on Macs, the external monitor connector on laptops is a standard VGA type, so you can plug your monitor in. If there are still lines, you'll know it's time for a new monitor or to see about service.
If you need a new video card, make sure you get one that will fit your motherboard. There are different slot types for video cards (PCI slots in older computers, AGP slots in newer ones, and PCI-E in the latest versions). This page
can help you figure out which you have if you don't already know. Once you get a replacement card, all you need to do is plug it in to the appropriate slot. The motherboard will detect the new card and start using it. (I'm assuming you'll be installing a card where there wasn't one before. Most consumer computers have integrated video and that's what you're replacing with a plug-in card. If your computer already has a separate video card, obviously you'll just swap the old one for the new one.) Also - this will sound obvious but it's amazing how often it's overlooked - you need to connect your monitor to the video connector on the new card. People sometimes plug their monitors into the integrated video connector out of habit. On some motherboards the integrated video still works when you plug in a new card, but on others the on-board video is disabled. Then you either have the same bad video, or none at all.
With a new video card, your display may look funny when you start Windows the first time. Until you install the drivers that come with the new card, the color depth and resolution settings may not be right. But with the right drivers installed, your display should be back to normal.
Hope this helps. Thanks for using Fixya!