Can I change the behavior of my firefox shortcut on the Windows 7 taskbar?

I have to admit that I've developed a nasty habit. When I want a new browser window, I shift+click the Firefox icon to make a new window of Firefox. Lately, though, I've been really wanting to get in the habit of just creating a new tab instead of creating a new window.

I'm wondering if there's a way I can change what the keyboard shortcut actually does, e.g. can I have it start Firefox with some sort of shortcut that would prompt it to start a new tab rather than a whole new window?

You have need to download the TabMixPlus add-on for Firefox.

After installing it you will find it under the Tools menu with the name of Tab Mix Plus Options. After launching the addon now see the Links tab and check/tick the option Enable single window mode.

Now under the Events tab select the Tab opening option and check/tick the option Middle-click or Control-click opens items in current tab. Now it will disable the control of Ctrl+T to open new tab and Shift+click will open the new tab.

If you want to focus on the new tab immediately then go to Events tab, Tab opening sub-tab, and in the group Focus/Select tabs that open from set the option Links.

Not quite sure if I follow the question but Ctrl+T inside of a Firefox window will open a new tab. Firefox support has a full list of keyboard shortcuts.