No sound through the built in speakers. Turntable turns fine and I can hear the record play but it does not transfer to the speakers. New needle makes no difference

you will an amp . this unit is supposed to a preamp., making it line level.
The Sony PS-LX250H's built-in phono preamp allows you to use the turntable with any receiver, HTIB, or computer sound card by plugging the turntable's cables into any line-level input, such as auxiliary or VCR. If your receiver does have a dedicated phono input, we recommend using it instead of the turntable's internal phono preamp (which can be turned off). Chances are, the turntable will sound better that way.
https://www.cnet.com/reviews/sony-ps-lx250h-fully-automatic-turntable-review/

Plug into auxillary turn to aux

is it possible your new reciever has a built in phono pre-amp?

If so, you need to switch off the pre-amp inside the turntable (lift up the rubber matt, and rotate the plate untill you see the switch at the back)

Try again now?

There will be some feedback from the turntable, and this is totally normal. Ive actually heard the music from the needle itself, and is nothing to worry about

Your tracking and anti-skate are not set correctly.

If you have the manual for this unit, it should have directions for setting these.

Funny thing about analog to digital recording without a preamp. You will record a signal, but that signal might be below the level of human audibility, if the line levels are left at the level that left the turntable, given the absence of a PREAMP.

Playing records is a contact sport.

Since the needle touches the record -- as opposed to a laser reading a CD -- any bit of dust or mold translates to annoying pops and hisses.

Record cleaners get down into the record grooves to extract dust and particles.

Or you may need a new needle.

either the cartridge is bad in the phonograph tone arm.  Or the pre-amp in the stereo is bad...remember that the turntable is the only accessory that uses the pre-amp input on the stereo.  I'm betting the pre-amp is bad.

I had exactly the same problem and followed the OP's solution, which worked, but I couldn't hear the track as it was being recorded.  So I tweaked the solution.  If you do the following, you don't have to keep changing System Preferences as you switch from record to listening:
Go to System Preferences, press the Sound icon, and click on "Sound Effects."  Then select the drop down menu and select "Play alerts and sound effects through selected sound output device" rather than the USB choice.  Then click on "Output" and select how you want to listen; I used speakers so I selected "Headphones" where the port is "Built-in audio."  Then click on "Input" and select the USB choice.  Now record a track and you can hear it being recorded through your speakers (or headphones).  When it's done recording and after the software transfers it to iTunes, you can play it again through your speakers without going to the preferences panel.  

If you cannot see a small tip on the needle then yes it is worn out,but you can check by rubbing your finger over the tip when the system is on,if you hear sound through the speakers then it should play the album,make sure that the weight at the back of the arm is set to keep the needle in the groove as this may be set to far back,move it forward to keep weight on the needle.

hope this helps.
CABLE GUY.