Dell os recovery tool and dell website cannot verify my tag

You'll need to take up the issue with the seller -- anything could have happened to the system in the almost 10 years since it was built.  Only they will know what.

You don't really need the factory OS - whatever version of Windows 10 it has is long out of date.  You can use the MS Media Creation Tool to prepare boot media for your system.

@ejn63​ i bought this  2 years ago , the laptop was in perfect condition , the only thing that maybe the dell factory os have better support , there isnt any major issues with the laptop itself , just with the service tag  "as you can see in the picture , the service tag is identifed the issue has to do with support service ", im just asking if the service tag can return to the service support ? 

Again, that's a question only your seller can answer.  And no, there's no advantage to the Dell factory OS since what you'd get is a generic image for the Windows release that came with the system.

If you need to reload Windows, proceed with the MS Media Creation tool.  You can still look up and download drivers by system model number at dell.com/support.

In the private Latitude 3580 Service Tag number, the first digit was the letter B, not the number 8.

This commonly happens with B/8, G/6.

Originally shipped from Dell February 18, 2017.

The corrected Service Tag number shows on the Support page.