It depends on what sort of file you're talking about, and what portion of the file you actually got. If you are missing the very first chunk you are missing the file headers and this will make things sort of tough. It can also depend on the application you're pushing this file through - some apps will go to lengths doing error recovery, others will just bomb out.
If this is important stuff for you, try to cobble up a header and stick it on. This means a lot of trial and error - go to www.wotsit.org
and try to get some understanding of the file format, then rip a header off an already existing file (of the appropriate type), stitch it on to your incomplete file, tweak a few likely variables, slide your data into appropriate spots and you might get a result. If it's something like an mpeg you'll probably find it's not impossible.