Hardware-wise only, assuming you have experience with such things as HDD removal and cloning, etc., I resolved the exact same issue for my niece in January. I acquired a CoolGear USB Multi-function cable. I already had one but having two just makes life easier. They are about $29.95 - I got mine from Amazon.com. The CoolGear has plugs for 2.5", 3.5" and 5.25" IDE as well as 2,5", 3.5" and 5.25" SATA drives. The CoolGear adapter also has a (MOLEX?) power receptacle so you might want to get a short 5.25" power plug to have on hand for those old 5.25" IDE/PATA HDD's.
If you have a working computer you can download MaxBlast from the Seagate website. MaxBlast was designed by Acronis for Maxtor HDD's but will work with any vendors HDD. I have gotten earlier versions in the box with a new HDD. I used MaxBlast on my working desktop to clone my nieces failing HDD. The new "clone" should drop in and boot up like nothing ever happened. For me MaxBlast was easier than Norton Ghost or Acronis True Image (of old) - very easy to navigate and within Windows not at a cryptic DOS-prompt like in the not-so-good old days.
You might be able to re-format the old HDD and use it as a USB backup drive with the CoolGear, or purchase a USB external drive enclosure and use it for non-essential stuff until it completely bites the dust. I got my 2.5" USB external enclosure from CompUSA years ago but I think places like TigerDirect and Amazon will have them. Just get the right enclosure for your HDD, that is, IDE/PATA or SATA. Good luck and if I completely missed the question, my apologies.