I have an old laptop I haven't used for a long time because I couldn't find my power supply for it. 

But recently I found a power supply that matched my laptop, but my laptop requires 19v 4.74 Ampere - and my new power supply has a output of 19v 2.37 Ampere.

Is that the reason why my laptop shuts downs when too hot or when I'm trying to launch some software?