As I said, you cannot get a service tag. Per the article,

Monitors without a service tag number purchased from resellers (Amazon, Best Buy, Buy.com, Cost Co, Walmart, Sams, other online store, etc.)
* Based on the monitor 20 digit PPID serial number date code start date, Dell will warranty the monitor for 3 years
* You must contact Technical Support for your country. Tell them to open the Dell internal only Oracle Knowledge Information center
* In the search blank, they should enter PNP13081, then click Search. This brings up the article =
Dell Monitor Replacement Policy and Procedure - Dell Global Policy

The customer is unable to provide a Dell Order Number or system Service Tag because the customer purchased the monitor from a retailer. The only information the customer has is the PPID serial number for the monitor. For monitors where there is not a Dell order number available, agents will use the date code embedded in the monitor PPID serial number to determine the start date when coverage started.

Discussion = The warranty will be 3 years starting from the embedded PPID serial start date on the label.
Solution = Set up the monitor replacement against the dummy tag.
* You would provide the following data to the representative if you ever need a monitor replacement within that 3 year period:
Brick or Online Store:
Monitor model:
Monitor 20 digit alphanumeric PPID serial number:
[Your]
Email address:
Name:
Shipping address:
Phone number:
Operating system:
Video card:
Video card ports tested:
Issue:
Troubleshooting performed:
* Monitor Factory Reset done
* Monitor failed Self-Test and Built-in Diagnostics
* Post further troubleshooting