check your alternator may be going bad
The same way you started it before replacing the battery.
Was it running before the old battery went south? Did you have a check engine light before you replace the battery?
A battery charger does one thing. It charges a battery, and starts with whatever charge is in the battery and goes from there. Running an automobile battery down will shorten it's life.
It is definitely caused by a problemtic cooling fan relay. When the bad relay shorts internally, it causes the fan to stay on at all times which drains the battery.
A 2.6A cell for a laptop battery means it is capable of outputting 2.6 amps of power per hour. This limits how long the laptop will stay powered on before running out of battery power.
There is a power icon on the taskbar. It shows whether the computer is plugged into the mains or on battery power. If you hover your cursor over the power icon, while it is running on battery power, it will show as a percentage how much battery life is left (along with an estimate of how much time you have left before the battery dies).
If the battery is fully charged and the starter is working properly it will turn over and start. The alternators sole purpose is to supply voltage to the vehicle and battery when the engine is running. When the engine is not running the alternator has nothing to do with starting the engine. If the alternator went bad and the battery was discharged then you will have to charge the battery before it will be able to start the engine. Do not jump start the engine with a dead battery if you can avoid it. This puts a strain on the alternator trying to recharge a dead battery and can damage the alternator, even a new one.
Sony claims that its standard battery for the VAIO VGN-P530H/Q provides 4 continuous hours of running time before needing a recharge.
Turns over but will not start or will not turn over? Is there a small wire at the battery, positive side that is not connected?
The Nintendo DS Lite Battery is a Lithium Ion Battery. They are known mainly for their long lifetime compared to other kinds of rechargeable batteries on the market. The Nintendo website claims that it can be recharged upwards of 500 times before running out.
Assuming it started and ran before you changed the battery, and changing the battery actually is when the problem began, the starter relay wire has been left off and needs to be connected at the battery terminal. I would need more information to diagnose it further.
My advice is to charge the battery with a battery charger before starting the engine. You will be putting a heavy load on the alternator if you allow it to charge a dead battery. This could damage the alternator.