Oldsmobile alero 2000 won't start

yesterday while I was coming back home,I had to pick up a friend so I parked the car in parking area without fully turning off the car ,but putting the right indicator and the ignition was on..so later when i turned off the indicator and turned the ignition again on ,which was already on the car wouldn't move so I turned off the engine fully and tried to start the car but it won't start at all..i called for jump start but the gut told the battery is fine...then had to tow the car to my house...The guy who was towing tried too,but it won't start..He says that it might be a problem with the alternator??is it?
When I turn the key all the lights come on ,the clock works in car,the service light is on,the low tire pressure light is on( this is being on from past 1 month even though the tire pressure is perfect according to manual..
I read in some forum that I should turn the key and wait for 10 min for service engine soon and other lights to go,I waited for 5-6 min but those lights were still there.I tried to turn off and tried to start the car again but it won't start...What's the solution?

Welcome to AF.

It would help to post your engine size and model Alero within the thread. You may have a Passlock problem which will prevent the starter from engaging and cuts off the fuel injectors. Is the security light on at the IP?

I haven't had the problem you're having, but I also read some posts about waiting ten minutes, and if I recall correctly, waiting 5-6 minutes won't do it, you have to wait the full 10 minutes.

Also, once you get this problem fixed, you can reset the low tire pressure light using the reset button located in the left fuse panel. With the engine off, key in the on position, push and hold the reset button for 5-10 seconds until the seat belt indicator blinks on the IP. Then push the reset button momentarily to cycle between the change oil and low pressure indications. When the low pressure indication is on, push and hold the reset button until you hear 5 chimes with the seat belt indicator flashing simultaneously. The low pressure light should go out. This also works to reset the change oil light, just hold the button while that light is on.

The low tire pressure light won't reset by itself when the tire pressure is adjusted, nor will the oil change light reset by itself when the oil is changed.

You must wait the full 10 minutes. I have had the passlock problem for 6 months now. You might try using another key that isn't very worn, sometimes this helps.
Read your owners manual for the oil change and tire pressure light reset procedures.
The service engine light will not go out on it's own, you must fix the problem first. Go to a dealer and have them scan the car to find the code that is causing the light to come on.