My Dell inspiron 6000 keeps turning itself off
It looks as if someone unplugged it and it went off
Sometimes it stay on for hrs and sometimes it just bling off without warning
What could have cause this? By the way my fan isn't working as it should.. I'm using a house fan to keep it cool
I know it didn't shut down because of overheating, because I checked the bottom of the laptop and its cool
What could be the problem?

It may be cool to the touch but the CPU may be overheating. That can cause the type of shutdown your talking about.

Quite a few things can cause it to just shut off...

As Califdadof3 said, just because it's cool to the touch doesn't mean the internal portion is over-heating...

What makes you believe a recent hardware/software change could have done this? I am not asking you because I doubt you, I ask you because it is very true... among other things!