Make sure that Windows 7 is fully updated to Service Pack 1. Run Windows Update until there are no more updates found. You may notice that there also is an update for your ATI Radeon HB 5670, even though you should check AMD's support website for an ATI driver update for your video card. If all this doesn't help the "lines", your video card may be dieing
Tmagic650 gave you some awesome advise, follow it to the letter and most likely everything will turn out fine. But just in case it doesn't work, try some "quick fixes", like seeing if your monitor has a (automatic image adjustment) feature, if so, engage it and a let the monitor re-adjust itself and calibrate and see if that cleans things up. If not, why not check your connections, make sure the end connectors are secure on the monitor and video card. Also if your video cable or cord is having to be bent around any corners or is being pinched in any way, in between the video card and the monitor, straighten out the cable and see if that does the trick. Also getting back to (connections) or (connectors) unscrew and pop off each end of the video cable or cord and make sure the end connectors are clean and free of any dirt, dust or film. If necessary, use a very small amount of (rubbing alcohol) and a (Q-Tip) and clean off the connectors, both connectors and ports, don't go nuts with the stuff and make sure if you need to clean your video cards video port, make sure the computer is off and allow about 10-15 minutes of dry time, before engaging the computer again. Also the last quick fix I've done in the past for misbehaving computer monitors is a very hard jump start! While the computer is on quickly unplug the power cord from the monitor, allow about 20-30 seconds and plug it back in, the monitor might freak out a little but that's ok, but it will have been given a hard re-set and hopefully act normally.