Blue screen error 0x0000007E,caused by ntkrnlmp.exe

"Unfortunately, I would suspect bad RAM long before I'd suspect bad BIOS, unless your BIOS settings had recently been changed. (Which you'd likely know about.)

While it may not be of immediate help to you anymore due to the ""no battery"" message, in this scenario, the first thing to do is perform a full-scale memory test. This will take a while on most machines. A great tool I've used for this in the past is MemTest86.

That test will let you know if it's bad RAM, which is usually a fairly easy thing to fix. (In fact, we were getting very similar behavior with one of my coworkers, and that's exactly what it was.)

Now that your BIOS is reporting no battery, my biggest question is: Are you sure you got the right BIOS upgrade? (Those are VERY picky. So much so that I can't remember ever even attempting one myself. Maybe once, back in the 90s?) In any event, even if the BIOS gets upgraded cleanly, you'll still probably want to do the MemTest to be on the safe side."