Power supply testers will tell you if the PS is broken outright, but won't tell you anything about how it might behave under load.
To troubleshoot a PS under load, one needs a voltmeter (suitable ones can be had under $10) with proper probes, and/or some straightened paper clips for connection. Measuring voltage should uncover the majority of likely problems.
To measure noise, one would need either a scope, or perhaps a sensitive AC voltmeter.--
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