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There is one easy thing to try before contacting Acer. 1) unplug power adapter from laptop, 2) Remove battery from laptop, 3) press and hold power button for ~30 seconds, 4) replace battery, 5) plug in power adapter, 6) start computer.
If that get's you nowhere, a little more info might be helpful.
Has the laptop been subjected to any unusual forces (ie. dropped or gotten wet or...)?
Has any hardware been changed or upgraded (even ram)?
Are there any lights when you attempt to start and if so which lights, what color and what are they doing?
Last, what model Aspire One?