How are the temperatures?

Download Speed Fan.
When you install it, run it and post the temperatures it shows.heres info it gave me:
Fan is running at: 2557 RPM
Temp1: 36c
temp2: 52c
HD0:38c
They aren't that bad.

I suggest putting an external house fan and face it at the computer.
See if that lowers the temperatures down and KEEPS the computer on longer.alright
what would normal, computer temperatures be?
My Laptop idles at around 50*C.

Your temps aren't that high but I just to make sure your problem isn't heat related. the temps actually rose..
38c
56c
40c
after being on a few minutes..
hasnt turned off yet.
ill GIVE it some time and let you know later if it helped.If it rose, that means your computer is heating up fast, which is probably why it is shutting down.
Lets see what happens. Keep your eye on the temperatures.

If you WANT, remove the fan and see what temperatures it goes up to and when it shuts down.Borrow a working PSU of the same wattage or greater and swap it in there overnite...
If the shutdowns stop replace the PSU...on SpeedFan when temperature 2 gets to 70c it shuts off..
the temp started rising really quickly after being on for a little while
it jumped from 52 to 70 in just over 15 minutes.
That seems to be the problem then...

Is that with the external fan or not?with.
it heats up fast either way, the fan doesnt seem to make much of a differenceI can't believe it's rising so fast and so high.

I think you will have to check to make sure all your computer is FREE of dust and it's not facing a wall or anything.
Also check the heatsink and make sure it's properly seated.

This is a recent issue, am I correct?