That's good, let us know if the new battery solves the issue.
And, on the freezer technique... make sure that you dry your L1020 completely before turning it on... or just make sure that it is completely dry at all times. The freezer method will drop the temperature of the entire unit (including the inner parts), and since majority of the parts of the phone isn't air tight and that the earth's atmosphere has a considerable amount of moisture in it (depending on where you are and what time of the year), droplets may form inside the device as soon as you take it out of the freezer. So keep it inside a desiccator or a bag of uncooked rice (or wheat) for at least 12-24 hours after leaving it in the freezer before trying to power it up.
But generally, I wouldn't recommend the freezer technique for electronic devices. The device is made up of different materials with different thermal expansion coefficients (how much a material expands or contracts depending on temperature changes). This means that certain parts would contract faster than other parts that may be attached to it. This may cause some warping, bending or misalignment which, no matter how minor, may jeopardize the integrity of the device. Also, certain materials lose some of their properties when cooled (such as elasticity) - even when returned to room temperature the property may never be restored (irreversible change). Hence, in all, the freezer technique may, for example, make it less resistant to drops or vibrations.