I’m assuming that you’re talking about a single archive that has been split into multiple files. If that is the case, then you can open the first archive file with your favourite prog (I recommend 7zip) and then choose some or all of the files/folders to be extracted. In this way you can extract parts of the archive until you have the whole thing.
Alternatively, burn all the parts of the archive to DVDs and then extract bits of them from there. Most decent progs will prompt you for the location of the next part of the archive if it can’t be found in the same location giving you a chance to swap the DVD or point to the other HDD.