If you haven't already unplugged the drive - do so now. The more you fiddle with it, the more damage you are likely doing to the platters.
The $350 guys are likely going to use a program called SpinRite or similar software tools which you could probably do yourself. SpinRite works but given the sensitivity of the date, you don't really want to use it as there is a possibility that it will do more harm than good.
The $1800 guys are going to crack open the drive casing, and try to read the platters directly. The guys I recommend for this sort of work is Ontrack Data Recovery. I very much suggest you use Ontrack due to the data in question - they will charge you around $1k.
Be very sure when you ship your drive to OnTrack to send it in appropriate shipping material -- padded sleeve, lots of bubble wrap.
Once you have your data back, allow me to recommend Carbonite an online unlimited automated backup service. This will prevent future heart attacks when (inevitably) your future drives fail and you'll never have to worry about whether you have a 'current' backup of your data.
Memory is a strange bell, jubilee and knell.
Stop rebooting immediately. All you are doing is causing more damage. If you are of a mind and are relatively techie there's one more thing to try. Remove the drive (carefully) and put it in an external drive enclosure. Boot a separate machine into Linux and try mounting the failing drive. If I lost you at "Linux" skip to paragraph 3.
If the drive can be mounted, it may be that it's only the boot sector that's toasted and your data is still there. Copy whatever you can from the failing drive to the Linux machine. Be smart, get the most important docs first: irreplaceable photos and documents go first, mp3s go last. Once you get everything you can off the drive you can either take it to a recovery service to try for the last files or call it good enough and chuck the drive in the trash. Your hard drive is now a rock. It's dead, Jim. Put a fork in it. It is now a paperweight. Any attempt to reuse it will only lead to tragedy.
Data recovery services can be sketchy. Some charge a minimal amount for a first try (which always fails) and immediately do the upsell to the $1500 service. Others will take a reasonable shot before charging more. I recommend asking around and looking online for references. Odds are some local Mom and Pop tech store will do a better job and be more honest with you than Geek Squad.
The good part is that there's no drive so damaged that you can't get some of the information back. The only question is how much time, effort and money do you want to spend on recovering the data. There are amazing stories about can be recovered from drives that have been erased, rewritten, even pissed on. If the data is worth $1800, spend $1800. If it's 95% mp3s and saved games, the hell with it. Get what you can and move on.
At some point in their life everyone has a catastrophic failure of the one drive that held all the really important stuff, the one drive that they knew they should back up one of these days but hasn't. Learn from this experience. Put a big-ass hard drive somewhere on your network and arrange for an incremental backup on a daily basis. Sign up for an online backup service. Me, I like BackBlaze because a friend of mine runs it and I trust Brian on technical issues and things relating to squirrels. Finally, if something is really important, make an extra backup. Email a copy to yourself and leave it on the server. Burn your entire home directory to a cd/dvd every month or so and stash the disk someplace safe.
Even if you can't get the data off the drive there are still ways to recover it. If you took digital photos odds are you emailed them to someone. Check your email account to see if there's a copy in your "Sent" folder. Failing that, email whoever you sent the photos to and ask if they still have a copy. Check through any old cds and dvds you may have burned. You may have copies or early drafts of some of your data. When you got this machine did you transfer files from another machine or drive? Do you still have it? How about your significant other, do they have any of the information?
In the end there's one thing you should do: find a local nerd and make friends. Ask around at work or the PTA meeting or the meeting of your Coven. Odds are someone you know knows something about tech and can help you out in exchange for pizza and beer. Keep in mind that requests for tech support are the bane of every techie so make sure you let it be known that you will compensate people for their help. The flipside is that most of us like helping people with their technology, so if you're cool, we're cool.
-=Logan
Research, facts, a Republican needs not these things.
Keep rebooting and listening to those clicks and you won't have to worry about data recovery.
It's been a couple of weeks now. What did you end up doing in the end? How did it work out? Let's hear The Rest Of The Story.
-=Logan
Research, facts, a Republican needs not these things.