First off, good for you for trying a Linux LiveCD!
The hard drive is indeed connected similarly to a desktop, just smaller. The only thing you may be able to manipulate is the connector from the motherboard to the drive itself.
Is the hard drive seen in the BIOS? If so, you could try running the free diagnostics from the hard drive maker's site, or SeaTools from the Seagate site if not sure.
Backing up the data across a network, or to a CD/DVD would be the best possible thing, because they absolutely will not save your data when replacing a hard drive. You could also get an adapter and slave it into a desktop machine IF the drive is not totally FUBAR'ed.
If the data is critical you could try a data recovery service, but that is expen$ive.