Toyota Avalon XLS 2000 Fuel Gauge and Compass

did you check fuses

Calibrate the compass built into the upper-right corner of the rearview mirror by holding the compass button (an "N" with two crossing lines) until your zone number appears. Determine your zone number by looking at the map in the owner's manual. Press the compass button until a "C" appears. Then drive in a circle three times at 5 mph or less in an uncongested area. The compass will automatically orient as a result of the circling.

Read more : http://www.ehow.com/how_5927729_reprogram-avalon-after-battery-change.html

Junkyard. Internet. Another Avalon owner---take picture with your cellphone.

have you checked fuses?if so its probably a relay/(switch)that needs replacing

Try a new battery. If current battery is more than 5 years old ,and after you charge it she doen't pass a load test ...its time to go.

See toyota technical service bulliten AC005-99.
This is a expensive repair but if you just unplug the the air inlet servo motor(behind the glove box )
the air should start to work but without fresh/recirc control.

ABOUT $500 US

You need to replace the A/C Magnetic clutch relay, located in the under hood fuse box. From the dealer, the part is about $80, though you can pick it up for a bit cheaper from your local autoparts store. It is a 2 minute fix, and a very, very common problem.

I looked up the codes you posted.
P0420 is showing a bad oxygen sensor on bank #1, the one down by the catalytic converter.
P0773 is an electrical problem with the shift solenoid E.
A bad oxygen sensor would cause lower fuel milage.