You mentioned that it only happens from time to time? Are you doing anything or have you been doing anything noticeable for it to start happening? Watching a video, something CPU intensive? Playing a game? Charging the laptop on the AC cable?
To begin with, it would be helpful to know what component it is that has failed.
- LCD screen: Start your laptop up and close the lid to turn the screen off once you have Windows running. You might need to change the "When I close my lid" option to do nothing to prevent the laptop from switching itself off.
- Charging circuit: Remove the AC cable and startup on just the battery.
- Battery: Remove the battery and startup on just the AC cable.
- Harddrive: Remove the HDD (harddrive), switch it on and leave it running. All the other components will still run, although you will only get as far as an error message sat on the screen. You could always boot into a live CD of Linux, if you wanted to surf the web while doing this test.
If you can determine the failing component from the checks above, you will know what to replace. If it is a battery or the harddrive, I guess you are in luck as you can do this yourself reasonably cheaply
If it is the power board or the LCD screen, repairs could be more expensive than the laptop itself as it is most likely out of warranty.
If neither of the above then it can only really be the motherboard. Again, not a nice thing to have to replace - especially on an Acer.