Hmmmm, not so easy then. Perhaps an association between Internet Explorer and gif files that's been lost from the registry at a guess.
What happens if you find a gif file on the forum, right-click and do "copy shortcut" and then paste that into the internet explorer address bar? Does that give you an "Open/Save" dialog which then opens the image in the browser in a new tab if you click Open? As a test I've used the gif file on the first post in "Advice for a loft antenna".
http://www.airnavsystems.com/forum/index.php?topic=3254.0tarbat, is your giftest.gif a blank image? When I click on it I get a new tab opened with a blank page and
C:\Documents and Settings\Andy\Local Settings\Temporary Internet Files\Content.IE5\JP8NDEND\giftest[1].gif displayed in the address bar.
I've found a page that claims it will restore Vista associations for various files. There's an entry for gifs. I'm not suggesting you run this straight off, but if you save the '.reg' file for gif, rename it to '.txt' then you can compare with your own registry entries. Ian this is probably not for you if you're not a "computer buff" as you put it, tarbat, I think you'll be familiar with examining the registry, right?
The registry entries that appear to relate to gifs and Internet Explorer are:
[HKEY_CLASSES_ROOT\giffile\shell\Open\command]
@="\"C:\\Program Files\\Internet Explorer\\iexplore.exe\" -nohome"
[HKEY_CLASSES_ROOT\giffile\shell\Open\ddeexec]
@="\"file:%1\",,-1,,,,,"
[HKEY_CLASSES_ROOT\giffile\shell\Open\ddeexec\application]
@="IExplore"
[HKEY_CLASSES_ROOT\giffile\shell\Open\ddeexec\topic]
@="WWW_OpenURL"
Oh, and just for completeness,
http://www.dougknox.com/xp/file_assoc.htm restores default associations for XP.