That "clicking noise" is affectionately referred to as the click-of-death by system administrators. This is typically a mechanical failure but can (rarely) be caused by a faulty controller circuit as well, or a combination(often one leads to the other). Taking into account the fact that it will not shut off unless you pull the plug, it may very well be an electronic failure.
The $1500 - $2000 option involves a company with the equipment and white room(immaculate dust free room) space available to take apart the drive and disassemble the drive platters. After which they use their special equipment to read the information from the drive and reconstruct it all in a usable format... The reason they immediately give you the caveat is if it's not a 'simple' mechanical failure and the heads(the little fingers that act like the arm and needle of a record player) either started spitting erroneous data every time it was turned on then it could have over written information, or, and more common cause for loss of data as far as I know, is that the drive head 'crashed' into the platters and caused physical damage to the data. Getting nerdy, sorry. You don't want to spend this kind of money anyway so lets move on to the other possibility.
I'm going to guess this drive is a few years old so you might have a little bit of difficulty finding the exact same model. Lets say that you can, whether it be
ebay, craigslist or what ever... You have a 2nd drive of the same model. Shop around all the computer stores in your area and ask them what they think about this idea until you find one that has either done it before or eager to try... It's a bit of a crap shoot because in order for this idea to work it must be only an electronic failure. The idea is to take the broken drives electronics apart and install the newer drives electronics in their place. You want a shop to do this rather then doing it yourself, unless you just happen to have an anti-static mat and wristband setup handy.
So the thing to be aware of(aside from the fact that it just might not work) is that if it is a mechanical failure it could cause the fresh electronics to not work(remember how I said one can lead to the other) so you could be out both drives... but hey, how many years of work did you say you lost? I've only done this myself with 2 drives, it worked for one and didn't for the other(the donor drive from the failure still worked afterwards btw). 50-50 is not so bad but 2 attempts is hardly statistically relevant.
Personally I'd go for the lab option if the data is that important. They will make you sign away your rights to even look at them funny as they promise that there is nothing they can guarantee because they typically offer this service to commercial clientele who have been known to party with a gaggle of hungry lawers - not because their methods are unreliable. The methods are reliable, the condition of the data is not.
In the future, aside from raids that are mirrored and/or striped sets WITH parity also think about burning every disk worth to a PAIR of double layer DVDs.
Why a pair? Because the 1st copy you keep at home or at the office - preferably not in the same building as your external drive(don't bother with a fire proof box, the heat alone will make them melt inside the box anyway) and the 2nd copy you send to mom. If you want to get extra paranoid, or if your data is exceptionally valuable to you, there are always safety deposit boxes.
Why double layer? Takes up half the space for less then the price of 2 single layer disks...
Burned CDs and DVD's are not an archival quality medium so they're not going to last generations on good will alone. Storing them in a cool dark place(box?) you can expect about 10 years out of them on the safe side. Don't forget to go back and copy them to new media when DVDs are replaced by TNBT. Probably sooner then 10 years if HDDVD or BlueRay copying becomes available to the consumer as quickly as DVDs did.
Good luck with the drive!