Merging two .avi (or .mpeg) files in to one?

I've searched google and these forums and I simply cannot find a suitable answer.

I downloaded a very large file a couple of days ago, which in total is about 1.4 GB. The file is split in to two roughly 700 MB files.

I use VLC to watch all my videos and whatnot, but I read that Quicktime Pro can be used to merge my two files. Unfortunately, quicktime simply locks up whenever I try and open one of the files. I've tried iMovie (where I cannot import the .avi's) and a few other small programs that I read as suggestions on either this forum or another.

None of these programs worked, and the two I had the most faith in - QT and iMovie - both failed to open the movie.

I would think that the files are corrupted, yet VLC plays them fine.

In an effort to make this easier for me, I converted the .avi's using ffmpeg to mpeg files. Yet I haven't had any further luck in merging the files.

I've tried redownloading QT (just restarted after downloading it, actually) yet there is no difference. Does anyone have any suggestions? Thanks.

EDIT---

I cannot edit the title, so I'm not going to edit the post... but instead of .mpeg's I converted the .avi's to .mp4's.