Thanks for the responses so far. This is just a quick update.
I find that the problem does not occur when using my desktop machine; also running firefox. So it appears to be specific to the laptop.
Both run XP and firefox (latest version).
Dave. 
Yes, Dave, but do they have the same security settings, are you running the same additional software (antivirus, anti spam, anti-pop-up, browser add-ons, plugins, etc. and all with the same settings). and is the laptop version of Firefox possibly corrupted, all of these can cause differences in behavior, and aren't necessarily going to be picked up by anti-virus scans..
First thing to check is your security settings in the browser and associated software. Those could fully or partially block scripts needed by the search function.
I run all kinds of blocking, so I don' even get a dropdown in the search box either for madmodder site on this page or the search the web box in upper right of browser window. Stilldrillin -- it is possible to have both.
BTW, David, I'm not clear yet which one isn't working for you.