Unable to associate file with pinned icon

This is my first post so please forgive me if I've put it in the wrong place. I have a desktop shortcut icon for a program that opens a specified file along with opening the program. When I drag that icon to pin it to the taskbar, the icon changes and the file is no longer associated with it. I must right-click the icon and then choose the file from the dropdown list. I would like for the pinned icon to be just like the desktop shortcut icon and to work just like it does.

Thanks Ztrucker. Here are the results of your suggested actions:

"Instead of drag, what happens if you right click on the Icon and select Pin to Taskbar?"

I right-clicked on the icon but there was no 'Pin to Taskbar' option to select.

"Also, right click on the icon on the Desktop and select Properties. See what is in the Target field. Repeat for the one on the Taskbar. They should be the same."

I right-clicked on the icon but the icon on the task bar does not have a Properties selection.

(Maybe I should have specified I'm using Windows 7 64 bit Home Premium.)

Thanks for trying! It obviously isn't a critical problem but I hate not to be able to make the machine do what I want!

Thanks, Bear. I tried that but still no luck. Very strange situation...