Before you look too hard for a repair shop, try this.

plug an external speaker into the speaker jack on the back, and see if 
that fixes it.

Or, push a plug into this jack several times, and remove it.

This is just to be sure that jack has not closed just enough to short 
out the receiver audio. I have seen that happen.

As for repair shops for the TS440, you need to be aware that many of 
the parts for that radio are no longer available from Kenwood, or from 
anywhere else other than another used TS440. So, most shops will no 
longer take them.

This is unfortunate, because the 440 is a fine radio.

-- 
Mike Duke, K5XU