To track the dispatch of Dell parts, you require the Dell Shipping Reference number.
This is referred to by technical support as the DPS Number.
The DPS Number is 11 digits long and starts with a country or region code. (for example, UK = 04)
All parts dispatched using technical support team are sent using UPS courier company.
You can track the parts sent using the UPS website
Image 1 - UPS Site
Image 2 - Tracking your delivery
See these Dell Knowledge Base articles for information about order and dispatch status: