hopefully it is just a cable issue! i'm not sure why because there's no moving parts, but cable problems are more common than some might think; I have lost count of the number of USB printer cables that have just stopped working (without any obvious signs of damage to the cable) mysteriously.
anyway, be careful about using the PS3's inbuilt backup system as your only backup system; remember your backup will be of no use to you at all if you try restore to a different PS3 than the one you backed up from. try to save as many unlocked saves, movies, vids and pics that you can to an external HDD too, just in case. (speaking as one who has recently been a victim of a fatal YLOD, you can never have too many backups :) )
safest but most expensive option is to get a new slim PS3 and do a PS3-PS3 transfer, but you'll unfortunately not have the old info on your old PS3 anymore as it would have been moved to the new PS3, and you lose out on the tasty goodness of the phats PS2 b/c, unless you keep the phat around and only use it on special occasions lol.