skiller1234 -
Welcome to CEG!
If your starter is cranking the engine properly, push-starting won't accomplish anything.
Replacing parts without doing any diagnostic work will just take time and cost money, with little hope of really solving the problem.
One place to start, since you have a 1995: You can easily dump the engine processor's error codes with nothing more than a paper clip (a scanner is required for 1996 and newer cars, which have the OBD-II standard interface).
Look here for more info:
http://www.contour.org/ubbthreads/showflat.php?Cat=&Board=trouble&Number=552342&Forum=trouble
I also like the Dali Design site. The free pages are enough to get error codes:
http://www.dalidesign.com/hbook/eectest.html
The error codes will help you discover what the engine computer thinks is happening when you try to start.
Also, for any sudden no-start situation, start with the basics:
Fuel
Ignition
Compression
And any time work has been done immediately before a problem, I'm always suspicious of what was done. Any possibility earlier repairs loosened a connector? The alternator is notoriously difficult to get to on Duratec-powered Contours. Make sure anything that might have been removed to access the alternator was completely and correctly put back together.
Other easy things to check:
Does the exhaust smell like gasoline after cranking for awhile? Is there any possibility the car has been bumped? Your car has an impact sensor that is designed to shut off the fuel pump in case of accident. It's possible the switch has been tripped (so no fuel to the engine). Your owner's manual includes a procedure that details how to reset the switch (IIRC, it's above the driver's kick panel).
Best wishes in getting it fixed quickly!