i suggest you try using the onboard video card. see if you can reproduce the same random lines when using the onboard video card with the same screensaver or 2/3d mode. if the random lines do not appear while using the onboard video, then its safe to say that its really your external ATI x1300 video card that is faulty.
does the random lines appear only after some hours have passed while using the pc and then you run a 3d program? it might be that the video card sort of "overheats" to heavier load of 3d graphics. check the video card's fan - ensure that its spinning fast and not blocked by dust or wires.
video cards are among the first pc components to fail after maybe more than 3 years of use. while we cant pinpoint for sure the defect triggers on the video card, you can try lowering the video settings to hopefully prolong the life of the video card.
1. ensure that your pc case has good ventilation. clean and dust-free internal parts and video connectors from the card to the motherboard, and at the back of the motherboard video port to the lcd monitor.
2. if possible, try lowering your color settings to 16bit. windows xp colors then wont be so pretty, but it might help prolong the video card's life.
3. some newer video cards and drivers allow you to monitor the temperature of the video card. if you have this option, see if there is a specific heat reading on when the random lines appear .