I have an AcerAspire 4830T. The power light is red most of the time when plugged in. It will not power on most of the time, even when plugged in several days. When it does, it is very randomly. Then may shut down at any time.
How long have you had it?
Could be a thermal issue. Turns off randomly to over heating? Next time you get it on download program called speccy and monitor the temps of everything.
When it does power on does it do so when plugged in? Or when running on battery.