Have you checked the battery voltage again to see if its charged or not?
If it's ok then the fault may be with the security PIC chip on the main board, the time & date settings are stored in this chip which the battery maintains when the machine is switched off.
The machine should still run ok if you are willing to put up with it asking for the time and date everytime it's switched on.The security chip supports the real time clock function as well as other security monitoring including when the machine is switched off,This would be a problem if the machine was still in commercial use but for home won't stop you using it.
I see, it has also started sounding the switched off alarm when turned on so your suggestion seems very likely . I will probably want to sell it on at some point so I'll have to fix it eventually, is it fixable or would it need a whole new board.
Without looking at the board a definite diagnosis cannot be given,but assuming now the fault is on the board and no repair(engineer) is available, replacing it would be the option.