Delving deeper
Simply being new doesn't rule out a bad/dead battery, but does make it less likely, so we'll assume it is okay.
How far do you get in the boot process? Does it die at the same point everytime? Does the notebook simply loose power when it fails or do you get any sort of warning before it happens?
You mentioned it dying before the screen has a chance to come up, so you aren't getting a chance to see if there are any warning messages first. If you have a video out port (and most nbooks do), connect it to a monitor and turn it on before booting up (rather than waiting for the computer to turn it on for you) and see if you get any kind of error/warning message first.
I'll also assume you've checked your BIOS and reset it to "factory default" to see if that makes any difference.
Also, you said the charger is warm when in use. How warm exactly? If the computer is only on for less than 5 seconds at a time, it shouldn't have much chance to get very warm.
PS: Another possibility- your cpu is overheating and the system is shutting down before it can overheat and ruin it.