The clock being wrong renders security certificates out of date. Online systems that set session cookies timeout immediately as you log in. Emails get sent with the wrong date and appear in the recipient's mailbox in the wrong order. With a date in 2003 they probably won't even see them.
You can reset the time every time you start the computer to get around this.
However discharged batteries eventually leak and damage the motherboard (often beyond practical repair, especially in laptops).