To me it sounds like the download is not complete. Try right clicking on the downloaded file (labeled Firefox Setup 1.5.exe or Firefox Setup 1.0.7.exe) then left click on "Properties" which will bring up a box showing some info, look for size which should reade 4.98MB if it is not close to this try deleting the file and then download from firefox's website again
May I suggest something positive?
Use your internet Explorer to search for Google New Zealand and once found add that page to your favourites or alternatively search for the Google toolbar and download it to your PC. Once installed it will appear at the top of your screen.
You can then customise this toolbar to suit your own requirements and it also has a "Search" facility which comes with it, which in turn does away with the need to access the Web through Internet Explorer.
I currently have this setup on my PC and I'm running Windows XP Professional.
Now to your Firefox and Thunderbird Downloads. I suggest you access the Mozilla site through Google and download these set up files to your desktop. I think you will find this more advantageous as the initial install wizard will ask you where you wish to save these files, once you action the install.
In closing, do not uninstall IE, as has already been mentioned some Web pages load better through this particular search engine. Personally I use IE as little as possible, because it it is a system download and not one I installed myself and therefore has a habit of installing some undesirable cookies at times.
I also run TrendMicro PCcillin Anti Virus, which picks up all these extra accessories which IE tends to bestow upon us.
I wish you well in your endeavours to stay safe in cyberspace and hope that the above may go towards helping you out of your dilemma.