Dead Hard Drive is Dead

My laptop finally gave up the ghost the other day and I've been running around like a chicken without a head since trying to get it fixed. The thing is still under warranty so Dell wants me to send it to them for fixing but my concern is that they're going to either reformat my hard drive or ditch it for a new one without giving me an opportunity to try to recover any data. With that said I'm making some last ditch efforts to get what I can from it tonight and tomorrow before I send it to them and any advice would be much appreciated.

Some technical details:

--Studio 1555 laptop if that matters at all.

--I don't seem to be able to boot at all while the hard drive is actually in the computer. I have a thumb drive with an Ubuntu bootable on it but even after changing the booting priority and disabling the hard drive as a bootable disk on the setup screen if I don't take the hard drive out the computer won't boot at all. It just beeps at me and freezes after POST like it usually does even though it should be booting Ubuntu from the thumb drive (and it does if I take the hard drive out).

--I got a SATA to USB cable and hooked the drive up to another computer to see if I could do anything with it but when I plug it into the computer I get a series of beeps from the hard drive. I also can't get the computer to recognize I've hooked a hard drive up to it even with the Disk Management menu (the desktop here is a Windows XP).

The symptoms make me think things are looking less than stellar for my hard drive, but if the problem looks familiar to someone and they have an idea of how I might get some stuff back from the hard drive I would be incredibly grateful.