I'm assuming you're attempting to open web page links / shortcuts. If Firefox is the default browser it should be opening as it has in the past and uninstalling another program should have no affect. it's likely something else was installed or changed that could of caused this issue. I'd suggest having Firefox check that it is the default browser.
In Firefox click Tools, Options, and click the Check Now button to have Firefox check to make sure it's the default browser. If it is the default browser and that does not resolve the issue what are the type of files you're attempting to open and I'm assuming this is Windows XP?