Since I could not recreate the problem on my computer, nor could my husband on his, nor could our daughter on hers (she uses a MAC rather than a PC), my husband turned to our travel computer, an old Toshiba. (I am risk-averse and, although it's backed up, I do not like to carry my laptop with all my work on it when I travel!) Lo and behold, when I tried to use Firefox to download an article from the center's website, it went into never-neverland.
After doing a quick web search, I found that this problem was mentioned more times than I care to know about and that there were more possible causes/solutions than I would care to decipher. The consensus, however, seemed to be that if Firefox uses its built-in pdf reader, there are certain pdf files that crash the reader giving a "stopped" message at the bottom. While sometimes hitting the back button and restarting would clear the problem (noted by one of my hard-working doctoral students who had figured this out last week), this approach would not always work.
Since many of my files are generated using the pdf generators in PCTeX and OpenOffice, I have no idea if there is a quirk between how those generate pdfs as compared to those generated by Adobe Acrobat.
The consensus solution (nothing like the wisdom of intelligent, geeky crowds), however, was to go to the tools menu of Firefox and, under options, change the program associated with pdf files to Adobe Reader. Changing this option cleared up the problem on my travel laptop, for the associate who originally contacted me this morning, and for several others!
On my usual computer and my husband's computer the association had already been changed which, I presume, is why we never saw the problem in the first place.
With computers, it may be several hours gone and only tiny steps forward. However, I managed to also get a neat code working today for an algorithm implementation for a network optimization model, and that was, in contrast, great fun and rewarding (but, then again, I had full control over that work and my progress)!