I own a 2010 toyota avalon limited & periodically the radio just stops working

SOURCE: 1998 Toyota Avalon with power door locks, front

Check this site out
you need the passenger side door lock assembly kit.
There is one posted for sale in the US on this site. just scroll down for the following information and link
Used 1998 Toyota Avalon passenger door lock assembly 1998 Toyota Avalon
passenger door lock assembly
this is the part that surrounds the lock driver side. Car color is green cary, North Carolina 27513
The solenoid or actuator arm for the door lock assembly is probably not working to full spec.

Hope this helps.

SOURCE: 1997 Avalon radio theft problem

Some dealers put the radio's antitheft code in the owners manual. If it's not there call your local dealer and they can reset the code for a fee.

SOURCE: speedometer in my 1995 miata stopped working while

Hi,
The reason for the speedometer not working should be the cable connecting the dashboard and the transmission.This could be caused by a problem on the speedometer cable. This cable is connected at the back of your dashboard to the transmission. Check out if the cable broke or has disconnected from the back of the dashboard. Thank you for contacting www.Fixya.com

SOURCE: i have a 1998 toyota avalon xls the heat and a/c stop working

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.

SOURCE: on my BMW 528i while driving radio stops working,

low power, bmw ecu has some code that starts shutting down systems on low power. so poor charging from the alternator to the battery.

this could also be a wet ecu tracking false codes.
i don't have direct experience with a series 5 but also check your ecu condition.

the ecu compartment is under the windshield on the passenger side on E36

you gain acess to it under the hood....
this compartment gets wet, the ecu lays on a flat surface in that
compartment.

the bottom side of the circuit board gets wet and starts corrosion.

remove the ecu, take the bottom plate off, clean the bottom of the circuit
board with alcohol and a soft tooth brush.

you should be able to see the signs of corrosion or conductive build up.

this gunk bridges solder points doing all sort s of wierd things to your
car, including false sensor readings from asc/abs controllers and other
sensors....

all the way to engine failure and worst case burnt and shorted wiring
harness.

I'm on my 3rd ecu, took me and the repair boys a few years to figure this
one out.

BTW: i would get that ecu mounted above that flat surface, use some sort
of standoff to raise it so that it is not laying in the wet.