Start with fuses then bulbs then wiring.
A force or acceleration
Critical acceleration is the minimum acceleration required to cause an object to start moving or sliding on a surface. It is the point at which the frictional force between the object and the surface is overcome by the applied force.
Start at the fuel filter. It may be clogged.
If the check engine light is illuminated, start with scanning for codes.
Bill pickett
You can start your 2004 Rodeo without a keyless entry key. Remove the keyless entry fuse and use your ignition key to start the vehicle.
If acceleration means to increase in speed or pace, then a stationary object is static, without movement, without acceleration. But, if an object is moving at a constant rate, then I suggest acceleration is not present, unless, or until the objects speed increases. Yes, an object with no acceleration may be stationary.
When you are stopped at a light, and it turns green, you start to drive forward. That is acceleration.
Low/bad battery, bad battery connection. If the battery isn't getting fully charged you might not be able to start. If it isn't getting charged, check the alternator.
Check the Rodeo choke to make sure that is closes when its cold. A bad choke will give you starting problems in the cold.
sounds like a crankshaft bearing, or a piston rod bearing are worn, broken or missing.