you have to keep in mind the a4000 is terrible in my opinion for airflow.
if you look at the design anything in front of the power supply partly blocks it.
when the case lid is on it restricts it even further.and it wont matter how strong the fan is...
if leaving the case off has a dramatic effect of making it stable,then there is your answer.
if the caps was indeed bad in the power supply they would still be bad no matter if the case was on or not,its that simple.
if you really want to know if the caps are bad just invest in a esr meter,and see for yourself.
to make a point if anyone looks at the power supply it seems to me it only keeps the front bay cool,lol
although, cooling is only one aspect of this.