Hello, First thing to check, see if bolts that hold the starter in place are not lose or missing. If they are in place and tight then it's problem with the Bendix drive of the starter itself. You will need to remove the starter and also check the teeth of the fly-wheel as well.
If the teeth of the gears are good, take the starter to be tested at Autozone for free, be sure to rule the other items out first before making the trip.
The only thing I can recommend in a no start situation is to check the parts that are common in this case. the crankshaft sensor located on top side of transmission under the exhaust pipe. be sure the wires were not damaged during strut change and/or are connected. Also check the camshaft sensor wires as well. Located on front of the engine. the other is if you have an in distributer coil you need to check for spark at one of the plugs. pull one out and ground it to the frame. have a helper turn car over and see if it sparks. if not change the coil and the only place I found to get one was eBay. don't fall for a distributer change if it is just the coil. the things you need to fire off an engine is air, fuel and spark. most common is no spark. those are the only three items to check for ignition since I don't feel it is a bad computer.
It may be that water/moisture has gotten in behind the door panels...do you notice that it worsens in damp(er) weather? The car unlocks by itself if you leave the key in the ignition and you try and lock the doors.
Or somebody has the same coded fob (unlikely).
You might want to reprogram the remotes if you determine that the area behind the door panels is dry and there are no corroded wires, etc.
2004 Nissan Quest Remote Programming
Note: You must have all remotes on hand when performing this procedure. Any remotes not used during this procedure will become inactive.
1. Close and lock all doors with the driver's side power lock switch located on drivers door panel.
2. Insert key into ignition (DON'T TURN) and remove it from the ignition key cylinder at least 6 times within 10 seconds (this will need to be done at approximately one second intervals). You may need to insert and remove the key up to 10 or 12 times until your hazard lamps flash. PLEASE NOTE: Withdraw key completely from ignition cylinder each time. If this procedure is performed too fast or too slow the system will not enter programming mode.
3. Insert key into ignition and turn to the ACC position.
4. Within 5 seconds, push the LOCK button on the keyless remote. Your hazard lamps will flash. PLEASE NOTE: Do not press the button on the remote more than one time or the programming will not be successful.
5. If there are any remaining remotes (including working ones), Unlock then Lock all doors using the switch on drivers door panel. Within 5 seconds of locking and unlocking doors press LOCK button on the next remote. Your hazard lamps will flash. Repeat this step for each remote (including any working remotes).
6. When all remotes have been programmed turn the key to the OFF position, remove keys from the ignition, unlock doors using the driver's side power lock/unlock switch and open the driver side door. Test all remotes.
Sensor A is the sensor for the engine cylinder bank that is closest to the radiator.. I have attached a link you need to look at that shows the diagrams of the sensors, the sensor A is the one next to the nipple that the upper radiator hose connects to and is labeled "Bank Two" in the diagram.
if you have it in neutral then the car will not accelerate
just the engine will increase in rpms
if it is a manual and in gear and you increase engine rpm but the car is not moving, it is more that likely a clutch master cylinder or cable problem
if automatic , run the fault codes and check for a problem torque converter clutch servo/solenoid problem