Can I connect a Dell XPS running Windows 8.1 to a Thunderbolt Display? Based on reading other questions and answers on your site it seems that this is possible. When I plug in the Thunderbolt to the Dell XPS via the Dells thunderbolt sized female input i get no response and am not able to "find" the Thunderbolt in the Display controls area.
I don't believe your "Thunderbolt" port on your Dell XPS is a Thunderbolt port, it's more likely to be a DisplayPort connector.
I'm not aware of Dell making any equipment that has a Thunderbolt port. Thunderbolt and DisplayPort do use an identical form factor, so it's easy to get them confused.
You cannot use a Thunderbolt display in a DisplayPort connector.
Since this answer was originally written, Dell has indeed added Thunderbolt 2 or 3 ports to their XPS line of laptops. Double check it is a thunderbolt port in the specs of your exact model and year, but a Dell XPS works well with my Thunderbolt display since the addition of a Thunderbolt port.
As far as I know you can only connect Apple Thunderbolt devices to the display for it to work. I haven't tried my display with anything else but I doubt it would work. When I run Windows 8.1 through Boot Camp on my rMBP it doesn't recognise the display at all so it seems it only works with Apple computers running OS X.