have to push car to start, after it runes a little and warms up it will crank. after a few hours after turning off it will not crank again. have replaced starter, battery , crank sensor , start relays

have a2001 tibron . problems starting. started when the gas tank would not take fuel on fill ups. cleaned the fuel lines and system . when removed  the charcoal canister all the charcoal came of the canister and the hoses. removed the gas tank and cleaned out all lines in the system. takes fuel o.k. now BUT is hard to crank when it is cold . I have to push it to start it. have replaced  the starter, altinator. battery crank sensor, starter relay fuses under the dash air flow sensor, have had it checked on their computer at the dealership with nothing showing up. when I first try to start it it turns over and then hesitates and trys to start again. after I start it by pushing it and it warms up it will start. after I shut it off for a few hours  will not start. after it starts it run great. I still have hair on my head and would like to keep it. hope you can offer a soulation Thanks John Cato