Hi Expert,
My Troy-Bilt TB32EC Weed Wacker won't start. The whole carburetor assembly works on another weed wacker. I also replaced the spark plug.

This trimmer has been making squeaky sounds when it was working.

What should I check next?

Appreciate any help you can provide.

Do you have spark at the spark plug when grounded to the metal block? 
 
Will it "kick" with a spritz of pre-mix down the carberator?
 
The fuel lines (especially the pick up), tend to break where they go thru the tank. Give a tug and pull out slightly to inspect the hose, very likely will look crimped down or just break off...
 
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I took the entire fuel tank and carburetor assembly from a working trimmer of the same type, but still not starting.  The spark plug also works on another trimmer.  This eliminates issues with these, right?

You have to check for spark on THIS machine.  Plug in the spark plug, ground to the metal block and look for spark...
 
Did you try a spritz of fuel as suggested?..