My desktop Acer Aspire L5100 (purchased Jan. 2009) was having sporadic boot problems, and then finally wouldn't boot at all. Upon power-on, there was no display from the BIOS or any other feedback on the screen.
I had seen some problems like this after the machine went into hibernation, but I don't believe that was the case here.
Upon doing a bit of Internet research, I opened the case and checked the motherboard's battery. After pulling one screw holding the DVD/HD unit, I uncovered the battery. The CR2032 battery only had about 1.5 volts instead of its 3.0 volt rating.