Starting issues
 

My Volvo S40 2001, don't start at once when starting motor drives the engine.
Starter motor needs to run for several seconds before the engine starts running.
This car has a manual gearbox, when I put it in second gear and push the car with another car and release the clutch, the engine starts running immediately.
I would like to know if somebody knows what could be causing this.
Thanks

The most common cause of delayed starting is that the fuel rail pressure bleeds off overnight, usually because of a leaky injector. If it's a fuel pressure problem, you can verify it by turning the key to the run position without engaging the starter, then off and back on again a few times. This will cause the fuel pump to run for a couple seconds each cycle (most times you can hear it, though barely). If the engine fires off immediately then, you have your answer (though then you have to decide if it's worth chasing the "fuel leak" or not).

The other thing I'd check is your battery voltage when you are trying to start the car. This time of year (cold) and a marginal battery can suck the battery voltage down so low when the starter is trying to turn a cold engine over, that it won't have enough juice to fully power the ignition (spark plug) circuitry. If the battery voltage "just sitting there" is below 12 volts, you need a new battery (unless the car hasn't been driven in days or has some sort of battery draining event going on). Even better would be to see if the battery voltage drops dramatically when you engage the starter - a quickie test for this is to turn on the headlights (pointing at a wall so you can see the beam), and see if the lights dim dramatically when you hit the starter. They will dim "normally" but shouldn't get a LOT dimmer.

+1 on the fuel pressure issue. A common cause losing fuel pressure in the rail is the fuel pressure regulator - a small but expensive widget on the end of the fuel rail. A quick test is to start the car up then shut off - pull the s shaped vaccuum line off the bottom of the pressure regulator. if fuel drips out, you have a torn diaphram which is letting the fuel bleed of the rail.

I have checked Battery and Fuel
 

I have checked battery and fuel rail, everything is OK.
The strange thing is: The engine start immediately if pushed or is running in a slope with second speed gear and releasing the clutch after the car accelerates for a while, some 10 miles/hour.
But if it using the starter motor, it needs to spin a lot of time. It spins a very good speed and the battery is a brand new one.
I was told that a defective camshaft sensor could cause this trouble. Someone knows if it could be possible?

I'm not sure why a camshaft sensor would work differently when starting with the starter motor vs. push-starting, unless it's a problem that only occurs when the battery voltage drops a little (like when you engage the starter). I guess the way to check if this is the case would be to hook a charger up to the battery so it's at well over 12 volts and see if it starts immediately instead of only after a few seconds.

does the car accept a jump start?

thank you Habbyguy and mt6127 for your help.
I did not tested yet if the power coming into the ECU, Electronic Control Unit, drops significantly.
Battery voltage did not drop any volt, because it is brand new and the starter motor spins very fast.
That's why I am so curious about this strange performance.
Once I will get rid off this problem I will post my findings in this thread.