Laptop turns off abruptly but sometimes it works

Hi!
I have a Dell inspiron laptop that keeps on shutting off by itself, though it does turn on sometimes and works for hours .But sometimes it shuts off the very first time, I switch it. It looks like someone is unplugging, when shuts down because its sudden. I don’t know what could have caused this?
Although my fan is busted , I keep it cool by an external power source fan. It’s not an overheating problem since I checked the laptop bottom and it is cool when it does that. Any help would be greatly appreciated.
Thanks in advance
