If you were to reformat, you'd only need to do the E partition - which would contain about 4.5gb, tops. Dunno how much spare capacity your laptop has, nor what the total capacity of your X-Box drive is, but you shouldn't need to backup the entire thing.
Usually this is caused by a corrupt save game - that is to say, if you backup just your UDATA/TDATA folders and then delete them completely, you'll probably be back in business (And then you can start copying saves back into it, some at a time. See if you can work out the exact file/folder at fault). You could even just
rename those two folders and leave them where they are.
There's a FATX limit of 4096 entries per folder, but given that there aren't even that many X-Box games, there's no way you'd've racked up
that many save folders.
This guy had a similar issue, though his game collection was very large. I'm somewhat convinced that the console only "likes" having 256 save games at any given time, though he never did any tests to confirm whether that was the case (just kept on formatting over and over for who knows what reason).