Winrar is the easiest choice for extracting incomplete files. However, it can only extract until the first missing part. I guess that's what you encountered.
Freeware programs that can extract broken Rar files are Tugzip, 7zip and Unrar for Dos.
There actually was a program that could replace missing rar partswith dummy parts, but it is no longer developed and doesn't work with Winrar 3.x (part01.rar) files.
If you encounter such a problem with split files (.001, .002 etc) you can use a program called Glue, which is a gui for Dedfiles. it's been years since I used it, but it worked. It creates dummy parts, which will enable you to extract all the parts that you do have