|When you boot up - is there "anything" on the screen at all; even briefly?|
Do you see the setup option to get into the bios settings?
When the system boots up - do you all the usual "noises"'; and are there "any" beeps that aren't usually there (the POST beeps that alert one to a given problem)?
A test that may help clarify what's happening...
Download and burn to DVD a ubuntu ISO (ubuntu.com); boot with that that DVD.
If it boots up - at least you hear all the usual noises.. - and no display then it points to a possible failure of the display adapter on the motherboard; a possible loose/broken connection between the display and the motherboard (not entirely unknown).
Presumably you went through the usual F Key combination(s) to see if you can get a signal to the external ports (Fn + F5); which toggles to external only or both internal and external (vga usually?) and back to internal only.
This is the "User" manual for Acer One series:
This is the Service Manual for the Acer One series:
Possibly either of the above manuals may also help resolve?