The starter perhaps?

If the engine cranks over normally when you attempt to start you car, but the engine does not start, the problem may be NO FUEL, NO SPARK or NO COMPRESSION. The engine needs adequate fuel pressure, a properly timed spark and normal compression to start. TIP: To find why the engine won't start, remove the air inlet tube from the throttle body, push the throttle open and spray a small amount of aerosol starting fluid into the engine. Crank the engine. IF it has spark and compression but NO FUEL, it will start and run a few seconds before dying. If it does NOT start, it probably has NO SPARK. TIP: Another method to check for spark is to pull a spark plug wire off of a spark plug (if it has plug wires, coil-on-plug ignitions do not) and place the open end of the plug wire near a metal surface on the engine. Have a helper crank the engine while you watch for a spark. DO NOT hold the wire while doing this as it can shock you. If you see a spark, the problem is not spark, but most likely NO FUEL or NO COMPRESSION. If you do not see a spark, the problem is in the IGNITION CIRCUIT. TIP: Proper fuel pressure is critical for fuel injected engines to start and run. You should hear the fuel pump inside the fuel tank buzz for a couple of seconds when the ignition is turned on (no buzz means the pump is not running and the engine is not getting fuel). You can smell the tailpipe for gasoline vapors after cranking the engine. If you smell gas, the problem is likely not fuel but NO SPARK. You can also remove the plastic cap and press the schraeder valve test fitting on the fuel rail to see if there is any fuel pressure to the engine (not a very accurate test because fuel pressure must be at a certain level for the engine to start, for that you need a gauge). Even so, no fuel at the fuel rail would tell you fuel is not getting to the engine.

could be the timing belt!

A screech usually indicates a loose belt. Instead of using a different belt for everything, modern engines use a “serpentine belt” to power the fan, alternator, power steering pump and etc. Re-tensioning a loose serpentine belt takes about five minutes and two tools and a little finesse. The belt is slipping,and as it does, it warms up, grips better, and the noise stops. Check the serpentine belt tensioner, it should have a scale (range) that shows if your belt is stretched beyond it's serviceable use, which could be the problem.

A screech, huh? Followed by the car shutting off? Not much to go on here, Lucky, but I'll try. First of all, check the oil level to be sure you have adequate oil. I doubt this is the problem, but I'd rather you NOT cause additional expensive damage to your engine if it is. Your car may have simply stopped coincidentally because it just didn't start up good enough to keep running. Next look at your serpentine belt (or several belts, if you don't have a car with a serpentine belt). This belt (or belts) are what make your alternator, Air Conditioner compressor, power steering pump, and water pump turn when the engine is running. make sure the belt(s) are in good condition and properly riding on their pulleys. Also, if you have one belt driving everything (a 'serpentine' belt), there is a spring loaded tensioner pully which maintains a constant tight tension against the belt to keep it tightly fitted against all the other pulleys. It is a small pully, usually near the power steering pump and alternator, about 4 or 5 inches in diameter. If it is going bad, it may be cocked slightly, causing the belt to rub up against a bracket or the engine. This will cause a squeeling noise while the engine is running. A bad tensioner pully will result in belt failure, which means you lose power steering, alternator, A/C, and most importantly your water pump (which will result in your engine overheating if you drive very long without it). A new pully runs about $20. A new belt about $20-30. To replace the entire tensioner will run about $100 for a new one. Now, about the noise: If the car made this noise just as you were trying to start it, then the problem may be your starter. This is a small electrical motor which first turns the engine over to provide the initial piston movement to compress the fuel/air mixture as the spark starts the combustion process to keep the engine running. Lift the hood on your car and watch the engine while someone trys to start the car: If the screeching noise happens and the engine does NOT turn over, then your problem is almost certainly a bad starter. The starter has a small gear on its shaft that is normally NOT engaged to the transmission flywheel. When you apply power to the starter (by turning your ignition key), the starter shaft rotates, causing this gear to move out into position and engage the gears on the flywheel. One of the failure modes of a starter is this gear sometimes fails to properly move into position. When this happens, you hear a really loud and annoying grinding sound which makes your teeth hurt. The good news is that a starter is relatively cheap to buy (anywhere from about $60 to $105 for my 1995 LeSabre) and pretty easy to replace. Replacement usually involves disconnecting your battery first, then disconnect the electrical cable on the starter, remove two bolts holding the starter on, and then reverse this process to install the new starter. There are usually one or two flat metal 'shims' betweenthe starter and the mount on the engine...just put these back when replacing the starter. To get to the starter usually involves getting under the car to access everything you need. If yo udon't know where the starter is located, you can look it up on a Haynes, Mitchells, or Chiltons manual for your car (about $20 for one at a parts store...or go to a local library). Alternatively, you can start at your battery and follow the fat wire from the positive terminal to where it connects to the starter. (Another fat wire will go from the positive terminal to the alternator). If the engine DOES turn over and a bad noise happens then you may have other more serious problems. It could still be simple, though: check for obvious visible signs of moving parts which should NOT be rubbing or listen closely to see if you can tell if it's coming from the power steering pump, alternator, A/C compressor, or water pump. If so, then replace as necessary. If the noise problem is internal to the engine, you will usually know it. I'm guessing, however, that since the engine will NOT run and it still makes this horrible noise as you try to start it, that the problem is something above, most likely a bad starter. Lastly, if all else fails, get someone who has some mechanical experience with cars there to help you figure it out. Or have it towed to a professional. Good luck!

My wife heard the same kind of screeching noise in her dryer, then I heard her scream. Our pet hamster who was lost for about a week was in there. I hope it's not the same type of situation.