Martin's hard drive died. He moved his images from his hard drive to the backup and a week later both of them have failed! What can he do? Leo says this is why he advises a "3-2-1" backup strategy: 3 copies on 2 different formats, 1 off site. That's why Carbonite is important, for the off site part of it.
There is one option after the fact and that's a company called DriveSavers. They can take apart the hard drive in a clean room, replace whatever parts are missing, and then lift off the data. Another option is SpinRite. Spinrite is only good for a limited amount of problems, though. It'll repeatedly read a drive that can be seen by the computer, and then will go sector by sector reading it and moving data to more healthy sectors. It's $90, and may or may not work for Martin, depending on what the problem is.
(Disclaimer: Carbonite is a sponsor).