When you install Firefox, it puts two shortcuts in your programs menu. The first one "Firefox" runs Firefox normally, and the second "Firefox [safe mode]" runs Firefox in safe mode (i.e it disables all the themes and add-ons, in case any of them are causing problems).
When you click a URL (internet address), Windows should run your default browser, and this is clearly not happening. It sounds to me as if you installed Firefox, set it as your default browser, then deleted it.
Open internet explorer
Click tools/internet options
Go to the Programs tab
Click the button (or checkbox) to make IE your default browser.
Then when you click your Blueyonder shortcut, it should automatically open in IE.