A friend reported she was having trouble with Firefox starting up, so we'll do a quick test. To start, press Ctrl + Alt + Delete and start the Task manager. Then, click on the "Processes" tab. Look at the list of programs, and you'll notice a number next to each "Process". This number is the amount of memory each process is using on your PC, the higher the number, the more memory it needs.
With Task Manager running, start Mozilla Firefox and look for a process called firefox.exe. Note down the number it shows after it has fully booted up.
Now open up Internet Explorer and look for iexplore.exe. Again look for the number. The lower number is the program that requires less memory to run (And should therefore run faster).
To fix a non responsive program at startup, check and see if you're having it open a large number of tabs all at the same time, or see how many other programs you have running at the same time. Both of these will slow it down. To change whether Firefox opens the tabs from last time or starts a fresh browser, go to Options>Preferences to change your settings.
Alternatively, I got rather annoyed when Firefox started running slowly on my PC, and I switched to Google Chrome, which I have been happy with ever since. You can get it here: http://www.google.co.uk/chrome
Hope that helps!