That's a biggie.
Well, it could be that your ON button isn't doing the necessary contacts and, of course, if it doesn't do the contacts nothing will happen.
It could also be a lot of things, the motherboard, the memory (though usually boots-very few cases where it doesn't), the powersupply (even with power indicators it might be broken).
BUT if what you mean is that you are getting a blank screen with no sounds.
Here is something I found on the issue:
Just go to the acer website and http://support.acer-euro.com/drivers/notebook/as_one_150.html
and d/load the bios update 3309, open the folder and copy two files to a
formatted fat usb stick. Rename the file FLASHIT to FLASHIT.EXE and
the second file 3309.fd(bios file) to ZG5IA32.FD rename them precisely
like that, please check your spelling is correct. Insert the usb stick
into the usb left hand side make sure the charger is plugged in . Hold
down keys fn+esc and power up the laptop, when the power led begins to
blink release the two buttons and press the power button just once,
observe the usb stick flashing indicating it's flashing the bios, please
note this can take a few attempts, I once struggled for a few hours
until I finally tamed the beast :) be patient okay, I would like to
point out if you wish to update within winxp use the same bios update
3309 , extract the zipped files to a formatted usb stick and rename the
two files again but DO NOT REMOVE or interfere with the other files in
the folder , with the laptop up and running open the folder and click on
the Insysdeflash file only within the winflash file, this will flash
your bios within windows and update it to the latest version, I read
that flashing it when using the fn+esc keys merely restores the bios , I
have tested this and mine updated to 3309 only when I flashed my bios
within windows using the complete d/loaded bios update as mentioned .
It will be worth reading the read me file to see what has changed in
this bios version, I can tell you that for those out there that have
password issues i.e. hdd set, the need to enter password with upper
case is not a requirement more and there are a lot more fixes too, enjoy
and I hope this bit of info was useful:)