For a problem like yours I try to make a copy of the bad drive as soon as possible. The drive is probably still in the process of breaking so we want to use it as little as possible.
The beeping sound concerns me. It may be too late or it might be connected to the computer incorrectly.
If you can try this and it works, I'll tell you how to do a recovery.
Download the ISO for Parted Magic from here and burn it to a CD...http://partedmagic.com/doku.php?id=downloads
If you do not know how to make a boot CD of the ISO, let me know and I will get you further instructions.
Put the drive back into the laptop (that way we are relatively certain that it is connected properly)
Boot the laptop using with the Parted Magic CD that you made.
When it gives you the list of options at startup choose...1. Default settings (Runs from RAM)
Once it boots, you'll see that it looks kind of like XP. Instead of a start button in the lower left it has a button with a picture of a hard drive on it. For this post we will call that the START
Go ahead open LXTerminal
and press enter
Let me know if it sees and lists the bad drive. Try to tell me as much of the output as you can or take a picture of the screen and post it.
Now you can shutdown the computer.START>Logout
Choose "Shutdown the computer
" and click OK
Does the drive beep in the laptop like it did when connected to the desktop?