A. Prime a starting fluid or carburetor cleaner in the throttle body to help the combustion, if the engine starts and runs until the starting fluid is ran out. Check the fuel system pressure.

The check engine light doesn't have to be ON to store a fault code.

B. Check the vehicle for fault codes to see if there are any sensors were involved to the malfunction of the engine.

1.Local auto parts stores such as Autozone ( not in California) or Advance Auto parts will scan and retrieve any diagnostic trouble codes ( dtc ) stored in the powertrain control module for free of charge..

2. Amazon.com has the code reader for less than $17.50 dollars + shipping.

3.Re-post the dtc's in here " answer question " for further assistance.

Note: we need the dtc's to identify the sensor, there are a dozen different sensors to operate the car.

Visit this site and see all the different sensors.

http://www.freeautomechanic.com/car-engine-sensors.html

Navigate to this site and see the code reader
http://www.amazon.com/.../ref=sr_1_1

Usually, the whistling sound may be related to; vacuum leaks (hoses cracked or damaged under the hood), air leak (due to windshield or window gasket or seal leak). First step - check the vacuum lines and hoses under the hood in the engine area.

It does sound like you have a bad alternator. I am very familiar with the 06 Rav 4 as one of my regu;ar clients has one that I have done some work on. I did an alternator on it last year and the first symptom she mentioned was losing the PS and the battery light was on. Your Rav 4 by the way, has ELECTRIC power steering which is why an electrical problem like a bad alternator will affect it.

Clean the throttle body and disconnect both battery cables and touch the battery cables together for a few seconds. As long as both cables are removed from the battery you can touch them together. Reinstall the cables, start the engine and let the computer learn the idle.

First step - have the check engine light or stored fault codes scanned - for free - at any local auto parts store; Advance Auto, Auto Zone, NAPA. Then, post a reply as 'add answer' for more assistance.

Possible Causes of Engine Hesitation or Stumble:

Dirty fuel injectors (cleaning the injectors often fixes this)
Dirty air filter (change filter)
Dirty / clogged fuel filter (change filter)
Bad MAP (manifold absolute pressure) sensor
Bad TPS (throttle position) sensor
Bad or dirty MAF (mass airflow) sensor
Low fuel pressure (leaky fuel pressure regulator or weak fuel pump)
Vacuum leaks (intake manifold, vacuum hoses, throttle body, EGR valve)
Bad gasoline (fuel contaminated with water or too much alcohol)

Sometimes, what feels like a hesitation is actually ignition misfire rather than lean misfire. The causes of ignition misfire may include:

Dirty or worn spark plugs
Bad plug wires
Weak ignition coil
Wet plug wires

Too many codes - as first step, erase these codes by resetiing the OBD memory. Pull (diconnect) the negative battery terminal for around 2-3 minutes. Then, reinstall the battery connection and start / drive the vehicle to see which code(s) come back immediately.

Often, the single code issue or problem may cause other codes to trigger.

These are all typical fault codes of a Camry. To rely on erasing codes by disconnecting the battery is not a sure thing and to give it the best chance of working, leave the cables disconnected for at least 30 minutes. Or, buy a code reader from amazon for $25 and read and erase them yourself anytime you want. Sure thing.
You do have to erase and see what comes back, but I suspect you will need at least one front oxygen sensor and one of the egr components is bad and is setting a P0401, but if iot does not return ion a few days then ignore it.

Local auto parts stores will this vehicle charging system with their mobile analyzer and they will provide an accurate answer for the car problem.

About $1000 to $1200 and yes the head has to be resurfaced but first should be tested for cracks.

Several possibilities; clogged radiator, collasped hose (lower), loose belt (faulty belt tensioner) to water pump.

Several possibilities; faulty starter, faulty starter solenoid, faulty / worn flywheel or ring gear teeth. When the starter is removed for the inspection, check the flywheel or ring gear teeth. This would be the large diameter disc on the back of the engine - next to the transmission - with the row of teeth on the outside circumference. Check to see if there are any worn teeth to cause the starter to not engage properly to turn the engine.
It is entirely possible the problem is solely with the starter motor - this can be removed and tested (for free) at any local auto parts store in your area; Advance Auto, Auto Zone, NAPA.

Check the many on-line auto parts sources, such as; www.autopartswarehouse, or www.rockauto.com for the replacement parts. For example, they (RockAuto) list the starter from around $85.00 for your vehicle.

Since its a leak in the 'gas' line, you should not try mending it. Instead you got to replace it asap. It may be a problem to do it yourself, but you can give it a try by using automotix.net/autorepair/diy/2008-toyota-corolla-repair.html. This includes repairing and maintenance techniques specially for you car. It should come in handy to you since you mentioned about being a single woman.