I bought the  EVGA 500 GD 100-GD-0500-V1  from Newegg.com.   It was not working .   I was building a new computer and got everything installed.  Went to turn the power on and nothing.  No PSU fan ran.  No fans in the case ran. Nothing.   To rule out an issue with a component or the motherboard, I plugged this PSU into an older computer that I know works.  Again nothing.   I am going to return it, but was wondering if this is a problem with these PSU?  I hope it is just a rare occurrence that I got a bad unit. 

Sounds like a bad unit..Happens sometimes no matter what brand or component.
 
You have 30 days from the invoice date to return it to Newegg for replacement or refund, otherwise, RMA it to EVGA after you Register your product, which you should do anyway.
 
See also: How do I test my power supply? in the EVGA FAQs. 

   It was a brand new unit.    It did not come with a test jumper.  I did send it back to NewEgg.   However, I cut the UPC Symbol out for a rebate, so that might cause an issue with the exchange.  

If you cut the UPC label from the box I will be surprised if they don't void the RMA at Newegg when they receive it and ship it back to you. Guess it will depnd on if they notice the label missing or not probably.   Have you already sent in the rebate form? 
 
https://kb.newegg.com/knowledge-base/return-policy/
 
 
Return policy
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