Well, if it can be made, it can be un-made...so yes, it could be physically broken. However, it may just be Windows flaking out (I have an old desktop that I've had on 24/7 for about 3 years now, and it occasionally has similar problems but with its USB ports. I finally got around to imaging a fresh install of WinXP on there, and all problems went away).
Can you look inside the port? Anything appear to be bent/broken (sometimes those pins can bend up--had it happen on a USB port before). The new cable is stiff because its, well, new--the cables have little bits of the metal housing cut and raised up to make a nice tight fit with the port so the cable doesn't just fall out.
Now, I know "reinstall Windows" is a crappy excuse, and I feel bad even suggesting it. However, if you do and the problem goes away, then it was just Windows acting up. However, if the problem still persists, and you've used both 2 cables AND 2 HD enclosures, then somethings broken and if its under warranty then by all means get them to fix it.
If its not under warranty (and you have the PCMCIA slot free) then pickup a cheap PCMCIA-to-Firewire card online somewhere. Should be able to find one for around $20-30 (give or take), which definately would be cheaper than having it repaired out of warranty.
--edit--Here is one for $26 shipped AR