There could be many different reasons why your car does not start immediately. If you did not test to see which of these things is the one causing the problem, or whether there is more than one cause; but instead just began buying parts and installing them; it might end up costing you much more money than was really necessary. Unfortunately, it is not possible to determine the cause of such problems without first testing the possible systems.
The first thing I would suggest is to have the battery and alternator tested. This can be done at low cost by an auto parts store that sells batteries and alternators. I would recommend a store like Costco, Auto Zone or NAPA; because they have better batteries than many of the other stores.
I would also have a cylinder compression test done. There should not be more than 15% difference between any two cylinder pressures. If the motor fails the compression test; it will have to be rebuilt or replaced. While the plugs are out, if the spark plugs have not been replaced in the last 20,000 miles; I would have new plugs installed; and would also replace the plug wires if your Rodeo has the 2.2 liter 4 cylinder motor.
If it passes the compression test; the fuel and air filters should be replaced, and the throttle body, mass airflow sensor, and idle air control valve should be cleaned.