Like most web authoring programs NetObjects has the ability to import a website from its location online.
However, it often mangles it in the process since it automatically tries to assign default page layuots to everything it pulls in and it may also decide to 'helpfully' add new navigation links to every page, whether you have navigation already in place or not.
There are ways and means around this though so yes, in essence you can import and work with the files on your web hosts server.
Why not wait until you get your laptop sorted out and post with details. It's pointless listing the necessary steps to use in NetObjects if you end up not requiring them and I'd rather not add to your stress levels by posting a lot of jiggery pokery ;-)
It's also worth noting that even if the laptop has died, providing the hard disk is OK you can simply remove it (usually two or four small Phillips head screws) then plug the disk into an adapter which allows its contents to be read and fully backed up to another drive in a desktop computer.
I regularly do this for clients who suffer glitches with their notebooks. The adapter fits onto a standard IDE cable in a desktop computer and the notebook drive slaves to the desktop master drive, allowing its contents to be read and copied to a safe location.
It takes moments to do and isn't exatly rocket science, so unless the hard disk itself has gone up in smoke your data could well be recoverable.
And yes, backups are important, aren't they ?