Lu,
Certainly sounds like the battery to me.
Be aware that some older boards had the clock and battery combined in one lump and may need it to be unsoldered for replacement, however most are just a simple, quarter-sized 3v lithium cell which can be changed with the computer switched on to avoid losing the CMOS settings. If you do this, just be careful not to short anything out by careless use of metal implements such as a screwdriver or tweezers. The output of the power supply and the board is only 5 and 12 volts so there isn't a risk of shock if sensible precautions are taken.
It's certainly not worth considering anything else to begin with.
As I write this, I have just removed the battery for my own motherboard with the computer running and conected to the internet.... It's a CR2032 type which probably costs about $3 in your part of the world. BTW, one thing just occurred to me as I removed it. Don't allow the metal battery case to fall across any exposed terminals or it may short something out itself. A piece of masking tape could be used to insulate the area adjacent to the battery socket. I removed my battery with my fingernail.
[ 02 November 2001: Message edited by: ShyTorque ]