Thanks Curious. The warranty has expired, it was good for only 12 months.
I just noticed something else. If I increase the screen brightness to about 75% of the max, it would go blank. If I decrease it then, the graphics would come back. This also works when it goes blank by itself, but not on powering up with AC plugged in.
When I ran Windows in safe mode for a few hours, it never went blank. Does it still sound like a capacitor or video/motherboard problem? About how much would it cost to fix it? Probably not worthwhile for a netbook that sometimes go on sale for about $250.
Increasing the brightness to compensate for aging can increase probability of failure. I've only owned desktops but I know they frequently advise to regularly use the battery to assure the it recharges correctly. Power up is the greatest strain for any system.
In safe mode the most basic 16-color graphics driver is used, allowing safest boot-up. For a desktop monitor the capacitors can be replaced, particularly higher priced older monitors with screws holding the back on. For some there are kits for replacing most of the power conversion capacitors for less than $25 retail. The monitor is separately powered and some boards can also fail.
For mobile systems the video and motherboard are combined and the cost is probably more than half of the new system MSRP for replacement. Capacitor replacement is more difficult but it is probably still in the video circuit. Fixing the ribbon cable connecting the video panel is described elsewhere but I'd say its more than 90% certain capacitors are failing. These have vents on the top to release pressure but visual inspection may not be conclusive. Power regulation is the most complex for mobile systems but I doubt the battery is involved.
Recover data and settings while you still can.