Saw this thread and wanted to post a potential solution, as I had the same problem recently:
You can try resetting your computer by holding the power button down for ten seconds, then releasing. The next step would be to open the computer and disconnect the main battery for 10 seconds to reset it.
However, if you keep the computer plugged in for long periods of time, especially if you live somewhere with a dirty power source (for example, I live in Mexico), your computer may have locked itself up to protect itself from a power surge. The good news is, this isn't a mechanical failure, it's just a security mechanism.
In this case, you need to open the computer, disconnect the main battery, and find a smaller, 3v battery on the motherboard that starts the BIOS (this is a small, round object just above the main battery on the MoBo that says something like "CR2032-3V-etc" and has a red and a black wire coming out of it). To reset the BIOS battery, you unplug it from the MoBo just like you did for the main battery, wait 10 seconds and plug it back in. Make sure you ground yourself before working on the computer.
If this solves the problem for you, then to prevent future failures, you'll need to buy at least a new surge protector and ideally a voltage regulator or no-break system, as this means you have an unsafe electrical current charging your computer.
Note that if you are still getting the splash screen (the Lenovo logo appears on your screen for a couple seconds before the computer shuts off), the error is probably somewhere else.