Time zones don't apply to the BIOS. You need to manually set the time/date there according to your local t/d. Normally, with a dead or failing CMOS battery, the t/d will reset itself to show the time and date when the BIOS software version was installed. Since this isn't happening, it is unlikely to be a bad battery (although you could replace it as a matter of course, they're not expensive).
You could check to see if you are indeed using the correct time zone, as there are several that use the same offset from GMT/UST, but which have local variations (such as dates of operation). In addition, check that you are not 12hrs out, as this is not always obvious especially when using the 12hr system. Finally, consider changing to another time server for your internet time.