Can't see it being a battery problem as you would usually get lots of advance warning of an impending "failure". You would at least get a CHECKSUM error at boot a few times. I also don't think the battery would cause a no boot it should just boot to the BIOS because all the settings would be erased. I guess its a cheap thing to try but I wouldn't count on it fixing your problem.
Like I said in my first post just use basic troubleshooting skills, either start from nothing and add until failure or keep removing things until it runs.
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