BSOD and lines typically indicate a failing card - I had this occur on my laptop with a discrete card.
1a) Try reseating your card after cleaning up your PCI-Express connector's contacts (both on card and mother board). Do likewise for the card's power connector(s).
1b) Try reseating your memory after cleaning the memory/slot contacts.
2a) If you're running Windows XP, try reducing Hardware Acceleration (under Display Properties) by one or two ticks.
2b) If you're running Windows Vista/7, try turning off the Desktop Windows Manager and Themes services.
3) Try underclocking your card by about 10-15% if you have the appropriate software.
If 2a, 2b, 3 minimizes the severity/frequency of the blue lines, it indicates a failing card.
4) Do you have onboard video or an alternate card that you can swap in, and see if things change?
I Had A Simular Experiance With A 7800GT I Had After It Had A Severe Overheat, And A 9600GSO I Had That Popped A Few Capacitors, Look At Your Card Closely And Check For These Blown Capacitors (The Tops Will Be Split), Most Likely Your Card Has Gone The Way of The Dodo.
I had this on my old PC, it was an ATI card (about nine years ago). I know exactly what you're talking about and it's so annoying! Luckily I had a spare monitor, I switched and used that. When I tried out the old one again it was OK. Spookiest 20 minutes of my life!