The paper clip test is useless to identify a properly working psu.
Verify that all of the psu cables are seated fully.
Since your old PSU works,
I think your new psu is defective and should be returned.
Why did you think you needed a new one?
What is your graphics card?
That is what determines the wattage you need.
Here is a handy chart:
http://www.realhardtechx.com/index_archivos/Page362.htm
Buy only a quality replacement.
Tier B or better from a list such as this:
Note: The PSU Tier List has been migrated to a new thread: https://linustechtips.com/main/topic/1116640-psu-tier-list-40-rev-10/ *** Welcome to the brand new PSU Tier List! Worked on, by @Stefan Payne, @LukeSavenije, and myself. This is a complete overhaul. We'd recommend that if you have a gamin...
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A cheap PSU will be made of substandard components. It will not have safety and overload protections.
The danger is if it fails under load, it can destroy anything it is connected to.
It will deliver advertised power only at room temperatures, not at higher temperatures found when installed in a case.
The wattage will be delivered on the 3 and 5v rails, not on the 12v rails where modern parts
like the CPU and Graphics cards need it. What power is delivered may fluctuate and cause instability
issues that are hard to diagnose.
The fan will need to spin up higher to cool it, making it noisy.
A cheap PSU can become very expensive. Do not buy one.