Compuitincolo,
This is a basic function of the realtime clock that tests the ability of programs to set and reset the RTC Alarm via the 06h and 07h interupts.
A real time clock alarm is a feature that can be used to allow a computer to 'wake up' after shut down or to execute tasks every day or on a certain day. It can sometimes be found in the 'Power Management' section of a motherboard's BIOS setup. However, some newer BIOS setups do not include an RTC alarm option, although it can still be set from within user applications. Wake On LAN, Wake on ring, and IPMI functions could also be used to start a computer after it is turned off.
I don't think the battery is at fault although swapping one out wouldn't hurt. I would check and see if there is a BIOS update for this machine and if so apply it and retest.
This function is critical if you want to make use of any of the "Wake on" functionality, if not it would not affect anything else I'm aware of.
-Fred