First, as Train said the voltage needs to be checked after the solder job of the battery leads.

Second, one of the ways for a tech to check a problem like this is to bypass the battery with the use of an external power supply. Most shops have adjustable power supplies that could be connected to the leads that came off the old battery. Since the lapper keeps time OK when AC is plugged in, the problem has to be either the battery, the leads connecting the battery to the laptop, or some point inside the laptop such as the internal connector pins, ribbon or etched runs on the motherboard up to the point that the 3 volts from the battery gets to the clock circuit or chip. Without the proper diagrams, it will require a visual tracing to follow where the 3 volts DC travels and the return path.