For the record update your post to include full system hardware specs and OS information.
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No beep codes, LED's, Q-codes etc. per the applicable motherboard User Guide/Manual.
Will the computer boot into Safe Mode?
Will the computer boot using iGPU (if supported)? (Remove GPU for testing purposes.)
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Power down, unplug, open the case.
Clean out dust and debris.
Verify by sight and feel that all cards, connectors, RAM, and jumpers are fully and firmly in place. Something could have been jarred loose during the move.
What else may have changed? Wall outlet, surge protector, power strip, extension cord - anything at all now different? Added, subtracted, changed?
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Who tested and how was the new PSU tested?
Remember that PSU's provide three different voltages (3, 5, and 12) to varying components. A fan coming on is not at all an indication of a fully functioning PSU.
PSU(s) - do verify that power cables from different PSU's were not mixed and matched.
Do you have a multi-meter and know how to use it? Or know someone who does?
FYI:
https://www.lifewire.com/how-to-manually-test-a-power-supply-with-a-multimeter-2626158
Not a full test because the PSU is not under load. However, any voltage(s) out of tolerance may indicate a faltering/failing PSU.