Fix a problem without buying a new case or what kind to get

Buy a case that has fans on the side, I usually don't spend more than $50 on a case and I really like my DiabloTek EPIC for $40. However they have replaced this model with the "EVO" i think it's called but it seems to have all the same features, it just looks different.

The job of a psu fan is only to protect the psu. Not to aid in case cooling.
Don't count on much help there.

Any psu should be able to be mounted right side up or upside down without problem.

Every psu I know of takes in air from the interior of the case and expels it out the rear.
If the fan is blowing air into the case, the fan is installed reverse to what it should be, and should be RMA'ed.
To verify proper fan operation, dangle a piece of tissue at the rear of the psu. You should see it blowing outward, not sucking in.
Do the same to check your other fans.

To see if case cooling is an issue, take the side covers off, and direct a house fan at the innards. If that solves your shutdown problems, then case cooling is an issue, and a $50 case will solve it.

Install hwmonitor and watch the temperatures of your components. Taking the side covers off and blowing a fan at the insides is a good idea, but actually knowing what the temperatures are will help understand if that is really the problem. My psychic debugging skills tell me that even if you do have a temperature problem, its not because of your case (though a case may improve the situation).