Its unlikely that noise on a modem would erase the program and hardware configuration. The battery is a backup for the PLC's RAM memory. As long as the PLC is powered, there is no need for a battery. You can even remove power for a few minutes and not lose the memory contents because a capacitor in the power supply module will maintain RAM. Your original statement that something happened over the weekend suggests to me that the PLC was turned off for a longer period of time than the capacitor can maintain the RAM. Since the battery was disconnected or not installed, you lost memory.