Hard drive beeps, not seen by computer

Product details: STBX1000101 Seagate Expansion Portable 1TB Hard Drive

Details of computers I have tried the drive with: all Win7, all with decent specs, all with internet connections to get drivers. I can provide more details if desired.

My problem has been occurring for a few months. When I connect the device to the computer, through SATA or USB, it makes a rapid beeping sound for a few seconds, then is silent (see my link). Sometimes my computer will make the noise it makes to signal it has found a new flash drive/cd/external hard drive when I plug it in, but this doesn't always happen.
The hard drive is not noticed by BIOS, Windows Explorer, or Device Manager, but it does show up in Disk Management. In Disk Management it is supposedly "working properly."

This is a link to an audio clip of what it sounds like.


Things I have tried to fix it: connecting with USB cable to multiple computers; data recovery programs (all the ones I've tried require the drive to be recognized by Windows Explorer); connecting it via SATA to multiple computers; using usb cords from other external hard drives.

No professional or invasive recovery has been attempted.

Things I have not tried but have heard of/am considering: freezer trick (put hard drive in freezer and data can be accessed while it's cold); drop trick (dropping it on the ground); shaking (rapidly shaking the drive back and forth using the wrist, along the axis of the disk's rotation); making a mock-cleanroom and investigating.

What I have speculate the problem to be: I see a lot of talk on the internet about clicking with regards to hard drives, but my drive doesn't click - it beeps. Based on what I've read from pages like this, it could be a problem with the spindle.

What I am willing to do: I am willing to destroy the drive - I don't care about the warranty. I have a couple hundred gigs of music, videos, word docs, and photos, but nothing essential. If you are going to suggest professional services, please understand that I won't be interested in paying more than one or two hundred dollars, so that probably won't be an option.

Thanks in advance.

 

Those beeps possibly indicates that the heads were stuck somewhere onto the platters (stiction) and are not properly parked into the head parking ramp. It may be possible to open the drive to place the heads into proper parking but that requires specialized tools and a clean room.

 

Thanks for the reply.

A friend suggested another fix that involved replacing the moving parts of my failing drive with an identical, new, working model. If the choice at this point is between a) sending it in to a lab and paying probably upwards of $500 to get it fixed with no guarantee of success and b) buying a new drive and some tools and either getting my data back or bricking the drive, I'll choose b.
Is there anything I ought to know before I make this decision?