I have 2001 pt cruiser wont start or crank I got a new battery and starter still wont start it all

Check starter relay.

check that the cam shaft is turning ( broken timing belt)
run the fault codes

DOES YOUR CAR CRANKS OR IS COMPLETELY DEAD ONLY LIGHTS? IF IT CRANKS AND DOESN'T ENGINE RUN THEN IT IS EITHER THE ALARM ( IMMOBILIZER )SYSTEM ACTIVATED,OR THE IGNITION KEY FAILURE. IF YOU HAVE A SPARE IGNITION KEY TRY AGAIN ( THE KEY TO BE THE ONE WITH CHIP INSIDE ).IF IT IS COMPLETELY DEAD THEN YOU NEED THE ASSISTANCE OF A QUALIFIED PERSON TO DIS ACTIVATE THE ALARM AND CHECK ALSO YOUR SMART KEY AS WELL .

does it start with a boost??
how old is the battery??
did you have the battery tested by a repair shop or CAA???
Problem can be as simple as a weak or dead battery or connections.

common car for starter problems hit the starter with a hammer while someone trys to start it if this works it is ure starter, if not the stater and neutral safety switch needs tested

It could be an ignition switch, ignition coil, starter, (most likely) or starter solonoid.

Common symptoms of a bad starter is fine starting when it's cold, hard starting when it's a little warm, and no starting when it's hot. The hotter the starter gets, the more power needed for it to crank. If you are experiencing these symptoms, the starter is bad.

could be ignition relays, starter solenoid...

needs a battery but be careful cause sometimes a bad alternater will cause the battery to go bad