If it runs for a while and then shuts down I'd bet on either an under spec or failing power supply, or overheating.
You have checked all the fans for dust and spinning at a reasonable speed? All case, CPU, video, and power supply fans.
Leaving sides off the case is in almost all circumstances not a good idea (ie anything other than in a rack in an air conditioned computer room). It disturbs the air circulation that the case was designed to have.
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