I agree, once your hard drive starts knocking its near the end - it's a hardware failure in the drive, and no software fix will correct it.
There IS a slim possibility you can recover it, I'll get to that in a moment. To answer your last questions first, I HIGHLY recomend that you get a program like Symantec Ghost or Drive Image. These programs back up an entire drive or partition into what are basicly big compressed (Zip style) files. They can write to one file, which is what you would do to tape, but a better idea is to "span" the image into 650 meg hunks. That way you can copy these pieces onto CDRs and have a very quick, easy backup of your whole drive. Ghost is included with Norton System works deluxe. I highly, HIGHLY recomend it.
As for Hard drives, 40 gig drives are selling for less than what 20 gigs were selling for a few months ago. I have seen them as cheap as $50 at Best buy, CompUSA, etc.
Now, as for saving your drive, here is how you MIGHT be able to do it. Now, you are probably fucked, so don't get your hopes up too much. but you have nothing to lose by trying. It sounds weird, but I have done this exact procedure myself in a situation identical to yours, and it worked.
1) First, take your bad drive out of the PC now. Don't turn it on again, it's only going to get worse each time. Set it aside.
2) Next, you will need a boot floppy. A Win98 boot disk works. If you want to save the entire drive contents, get a program like Ghost, and set it up to work from a boot floppy. If any of your drives are formated with NTFS, get a driver program that will allow you to read NTFS from your boot floppy. There are a few you can find on download.com - I use NTFSDOS, a free read-only version is available. Test that your boot floppy works by booting your machine with it, and making sure that you can see (and write to) your second drive.
3) Now the fun part. Put your damaged drive into an anti-static bag. Seal it air tight, and try to get as much air out as you can. then put it in the freezer. Yes, IN THE FREEZER. About 1 hour should be sufficent. While it is in the freezer, make sure your PC is open, and arrange it so you will be able to quickly plug the drive in and power the system up. This little maneuver usually only works once, so make sure you are ready.
4) After an hour, take the drive from the freezer and quickly install it in the PC. Some moisture (condensation) may appear on the outside of the drive - don't worry about it. Boot the computer up with your floppy. DO NOT try to boot it with your bad hard drive.
5) With luck, you can now read the bad drive, and will be able to until it heats up (a few minutes). If there are just a few files you need, quickly do a copy from the bad drive to the good drive. You will lose the long file names, but you can rename them later. If you want to try saving the whole drive, quicky start up Ghost (or whatever you are using) from floppy and start writing an image from the bad drive to files on the good drive. Ghost can compress about 2 to 1 average, although files that are already compressed will not compress any more. So if your 20 gig drive had 10 gigs of files, you will need at least 5 gigs of space on your second drive. Extra space is of course prefered.
6) If it works, pat yourself on the back and call yourself a genius. If it fails, well - the computer Gods just had it in for you.
In the future, I HIGHLY recomend that you write a backup image of your system drive to your second drive at regular intervals. I have 5 PCs in my house, and every single one has a system drive and a second, larger data
drive plus a CDR drive. About once a month (longer if it's a PC I haven't made changes to) I write backup images. Since the second drive is a data drive, I just back up those data files straight to CDR.
Hope this helps. I had heard about the freezing trick a long time ago, was skeptical, but always figured I'd try it some day. About 2 months ago a PC was brought to me with the exact same situation as yours, and I'll be damned it it didn't work just as described.