Might be the "CMOS" backup battery playing up. Is the date and time correct if you disconnect the main battery and AC adapter overnight.
Other problems might even be "physical" such as an intermittant or cracked PCB print around the AC adapter socket. What if you power it off at night (while running on AC mains), unplug the adapter but dont disturb anything. Will it power up then next day ?
It could be many things.
Have you removed the battery and held the power button for 20 seconds or so to "reset" the logic by discharging any capacitors.