My wife's Aspire 1 kept shutting down on start up. I noticed the battery light was yellow, not the usual green. I borrowed our daughter-in-law's ACER power supply for a laptop (same interface but bigger power supply). It booted right up with the larger power supply.
After about 10 minutes, the yellow battery turned green. I swithed the power supply back to it's original smaller supply and the laptop worked fine. After about 20 mintes of charging (while on), I was able to cycle the power on the netbook and it worked fine.
It appears the ACER Aspire 1 netbook does not want to boot up if the battery is too weak. The larger rated power supply apparently had more power to spare for booting up. The power supply that comes with the Aspire 1 netbook must be a bit on the weak side. It is best to plan ahead and keep the battery charge or get a bigger supply (use one from a larger ACER laptop).