Toshiba L55-B5396 works fine with the battery out. After being unplugged it needs the date and time to be entered in the CMOS setup. Seems like something is wrong with the RTC battery, but I can't find that on the motherboard.
Thanks for your fast reply. I know that the main battery is ok, so I guess I need a new motherboard or computer.I've found some models (including Toshibas) just don't have a CMOS battery, relying on the main battery for that, in my work as a tech. That may just be how the system was designed.