Does my MacBook have malware? Frozen screen and Automatic Clock Reset on Macbook Pro
The date was lost when you let the battery run flat. Once you reset it, it should be fine.

Check out Adware Medic (donationware) for any other PUPs, then run Avast again to see if it finds anything else.

Read http://www.thesafemac.com/mmg-defense/ too, to see what you can do to protect yourself in future.