Can a new Sony TV with no audio out jacks have external speakers
added. I have a Sony receiver that I connected the speakers to on my
old tv which had output jacks but the new one has no output jacks or
any audio jacks. The old set up was--TV connected to Receiver
--speakers connected to receiver.

Please give us more info about your setup:

TV Model

Do you have cable/satellite.

Do you have a VCR or DVD as part of the set up.

etc etc....

(Ultimately you'll likely need to connect a coax to a VCR or DVD and
run your speakers from there but let us know more about your setup)

Canadianhelper is right.

I have the same problem with my TV.

I have my antenna hooked up my VCR and the audio-outs from the VCR to
the receiver.  My video-out goes the receiver as well. Also the audio
and video from my DVD play go to the receiver.  My receiver has the
video out to the TV.  This way I can switch from DVD to VCR with the
remote for the receiver and always get the sound through my speakers. 
The only downfall is having to turn on the VCR and use it to change
channels when watching TV.

Some receivers let you plug your coax cable right into there and then
pull a coax out to your tv. That way the receiver picks up the sound
directly from the coax.

If all else fails, you can run external speakers off of the earphone jack.