It's very rare for a CMOS battery failure to cause a problem like this.
The CMOS battery only powers the RTC/CMOS when the system is off AND the
battery is out AND the power is disconnected. On a desktop, with the
advent of ATX power supplies, the RTC/CMOS is powered by Vstby, as long
as the owner doesn't make the mistake of turning off a power strip that
the machine is plugged into.
Still, if you can find the CMOS battery it wouldn't hurt to replace it.