No. It's highly *unlikely* that it's your battery.
Two points:
1. A weak battery might cause some loss of time--perhaps a few minutes every
time you powered off. It would not cause only the year to change.
2. Before anyone whose clock is running slow rushes out to buy a new
battery, he should first take note of whether he is losing time while the
computer is running or while it's powered off. If it's while powered off,
the problem *is* very likely the battery. But if it's while running, it can
*not* be the battery, because the battery isn't used while the computer is
running.