You'll just about have to have some sort of video editing software. I like Roxio VideoWave best for this kind of thing on the PC side... I assume iMovie or Final Cut would be the option on the Mac side. Add the two video files in back to back, trim off any dead space or credits off the end of the first and beginning of the second. Then, let the system re-encode them into a single file.
That'd be about the only option I know of.