Hi, I'm new here and I would appreciate it if someone could give me some feedback on this as I have not much of a clue with computer hardware.

About a day ago, my computer (an almost 3 yr old Acer Aspire 5680 with a NVIDIA GeForce Go 7600 256MB graphics) just blacked out on me, totally shutting down. And, when it started up, there was green vertical lines while the window logo was at the background and it was loading. Then, there was a flash of a blue screen with some words on it and proceeded to prompt me if I wanted to start it normally, on safe mode, safe mode with networking, etc.

So, I tried "Start windows normally" and it did not work. It restarted again. There was also some distortion on the images. Then, I tried it on "Safe mode with networking" and my computer works just fine except for the poorer image resolution. Hence, now I can work on Safe mode but view videos without audio.

Can anyone tell me if this is a hardware problem? I suspect it is the graphic card problem since my computer shuts down on me whenever I'm playing games or loading a few videos at once, and the back of the laptop where the fan is, is very hot.

This has all the makings of a failing screen, based on your report of the green vertical lines.
Otherwise, you have a hardware failure of the nVidia GeForce Go7600, which cries for replacement.