How do you know when the video card is going?

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Thats hard to tell but in general a bad video card will exibit video tearing and distortions.
 
My laptop displayed coloured lines starting at the bottom and moving up. The audio keep playing, but there was no video. So I rebooted. It was fine for a few videos and then the lines appeared again. I left it running (didn't reboot) and it want back to normal. Please note this happened after I was running the laptop for 12 hours.

The next day I ran the laptop for 5 hours and all worked fine. Suggestions?

Do video cards over heat?
 
This sounds more like a display problem. The display power invertor is failing. If you look it up on google it will explain a bit more.
 
When my first video card died... wait... the first video card I had that died... yeah thats better. Anyway. It started turning everything into multicolored negative images. Like the negative of a photo, but looking like the bottom of a bad 80's skateboard... all neon pink and green and white. It was overheating, and I didn't know it at the time. I continued to do things with it, just thinking it was graphics glitches, but soon after, I couldn't get any image at all.
My last card that died happened to be a $600+ card. An EVGA geForce 8800 Ultra KO Edition, not long after they came out with them. Lightning storm. Even through a surge protector it fried the cable modem, my motherboard, and the graphics card. The PSU and the CPU were both fine though, which actually had me laughing a little.
 
Usually it starts with the video card wanting to hang out less and less, then you notice the video card is texting someone all the time and doesn't let you see who, then the video card uninstalls itself from your house and sends you a "dear john" letter.