This happened a long time ago...as in about three weeks ago, but I got my Acer Aspire One back.
Acer replaced the motherboard. They did not say what was wrong with the motherboard or why it happened. However, on the positive side, Acer did not restore the hard drive to the OEM state...which means that I did not have to reinstall Ubuntu.
I hope that I do not have any more serious problems (ones that I cannot fix myself). My warranty expires at the end of this year. I really do not want to buy an extended warranty.