Have a2001 Saturn sw2 lacks power when accelerating and crushing but when you pass half throttle it will go better. I've checked fuel press.it is 50_55psi and at low speed and idle runs great

SOURCE: Noisy engine idle and stutter at low or high speed

I had the same problem (X-type 2.0d 2004). The stutter was cured on mine by getting the ECU fashed with the latest firmware. This is a known problem and the update does cure it (£28), I didn't bother with all the tests the garage wanted to.
The noisey engine at idle is the alternator belt. It resonates at idle and causes the noise, There is a modified bottom pulley, tensioner and belt kit, but it is rather expensive ~£200 plus fitting (around 4 hours labour). Mondeo's have the same problem but that kit doesn't fit the Jag.
Hope this helps
KB

SOURCE: fuel/accelerator problems. dies when accelating or at idle. runs when accelerator held in one position for a short while.

CHECK THE IDLE SPEED SENSOR, UNPLUG IT AND SEE IF THE VEHICLE REVS UP A BIT. IF IT DOES, THEN REPLACE IT. ALSO CHECK THE FUEL PUMP RELAY IN THE FUSEBOX. HOPE THIS HELPS. .LET ME KNOW. GOOD LUCK

SOURCE: S10 blazer lacks power, bogs under acceleration

Check your coil output, buy a cheep spark tester. Pull of a spark plug wire and plug in the tester(ground the other end), set it to bridge a gap for 30,000 volts.Have someone start it and make sure the spark will jump the gap on the tester.Danger-Very high voltage! It will light you up if your touching the tester while the car is running!You'll be able to see a bright blue spark(and hear it as well) if your coil is good.If it's a yellow thin spark it's probably the coil.
If you have good spark, check the fuel filter and fuel pressure at the fuel rail.
Back firing could be timing,cam position or crank position sensor.Worst case scenario, timing chain or belt.

SOURCE: 1994 toyota corolla has a runs rough at idle and

I have a similar problem with one of my Toyota Corollas. It's a 95 model with the 1.8L engine (7A-FE, automatic). But unlike yours, it has plenty of power while running. Here's what it does. Occasionally the engine misses. Sometimes it will die. This is most likely to happen when you start the car and put it in reverse and start rolling without giving the engine time to adjust. I've been told by some customers that it will die sometimes when coming to a stop. But this has never happened when I drive it. I don't think it's a fuel issue because the car runs just fine when it's running.

Here's what I've tried so far:

1. Replaced spark plugs and wires.
2. Used gasoline additive fuel injector cleaner.
3. Checked air filter.
4. Checked vacuum hoses for leaks.
5. Replaced PCV valve and hoses.
6. Cleaned the air intake and throttle body with carburetor cleaner.

1. Check the throttle position sensor.
2. Check the MAF sensor.
3. Adjust the idle via the set screw.

SOURCE: Rough Idle/Runs Rough and low power

I would take it in and have them do a diagnostic on it, sounds like the cam shaft sensor to me.