Crucial does not have a listing for the 7620, but they do for the 5620 (likely uses the same system board).

• CT32G4SFD832A

In addition to what @ejn63 has posted, the 7620 RAM configuration is a bit of a different beast. As per the specs here, 1 x 8GB RAM module is integrated on the MB. There is one slot for RAM and the RAM is DDR5 4800. The RAM module you posted should work unless there is a compatibility problem with the integrated 8GB module.

Just for comparison's sake the RAM sold by Dell and listed as compatible is here, but at a very premium price.

That's DDR4 RAM. The Vostro 7620 mobo uses DDR5. Not compatible.

Kingston website states this is compatible with the Vostro 7620 --  KCP548SD8-32. Received it today, doesn't POST either. Very frustrating.

DDR5 RAM seems more finnicky that earlier types. Sometimes a seemingly-compatible stick won't play nicely with other RAM.

Anyway, it's worth trying this:

Use a soft pencil eraser to clean all the contacts on the RAM stick.
Moisten a microfibre cloth with 99% rubbing alcohol and use a credit card to slip the damp cloth into the RAM slot to clean its contacts.
After everything is dry, insert the new RAM stick firmly, ensuring that it seats fully in the slot.
Then boot into BIOS to see if it's recognized.

Thanks for the suggestion. Cleaned the contacts with compressed air and rubbing alcohol. No dice. The stick is firmly planted. Doesn't POST at all. Only keyboard backlit is on, nothing else. Once stick is removed, it POST just fine.

 That’s too bad. DDR5 RAM is much more particular about matching with other sticks. Often combinations that should work do not. 

Thanks for posting this info! Definitely saved me from a headache. 

I believe I have a solution, samsung is one of the manufacturers for Dells ram. From everything I have found this is oe equipment not branded dell.

Samsung M425R4GA3BB0-CQK

I was able to pick it up on e*ay for $150 but will not be able to try it until my laptop comes in August 1st!

If you want a store front check out Memory.net for SNPR62CWC/32G or the above samsung number. I will update when tested.

I just bought that Samsung M425R4GA3BB0-CQK from eBay for $150. No dice, doesn't POST. I have a Dell tech coming tomorrow with a new mobo. May be defective mobo.