@bones1 , Randy, Speaker relay on the power amp assembly may be faulty or the Amp it self, faulty volume switch(disassemble and clean/replace). Below is a good link for you to check out about restoring the Kenwood Receiver with some instruction on checking speaker relay, etc. 2nd link is a trouble shooting forum for same issue as you are experiencing. Good luck.
I hope this helped you out, if so let me know by pressing the helpful button.
http://www.vintageaudioaddict.com/kenwood_eleven_iii/kenwood_eleven_iii.htm
http://audiokarma.org/forums/index.php?threads/receiver-with-power-but-no-sound.415300/